Suppose Tom Harmon17 is standing at the exact center of the Ohio State football field18 on the 50 yard line. The field is 300 feet long and 160 feet wide. Suppose the ball leaves Harmon’s hand at a height of six feet and has initial velocity v(0) = 40i + 39j + 32k feet per second where j points toward the sideline, i points toward the end zone, and k = i × j points straight up. The acceleration due to gravity is −32k feet per second squared and the mass of the football is .45 kilograms.
(a) Determine a parameterization for the position of the football at time t seconds after it is thrown.
(b) Suppose David Nelson19 catches the ball when it is six feet above the ground. Is Nelson in bounds or out of bounds when he catches the ball? (Assume Nelson’s toes are touching the ground directly below the ball when he catches the ball.)'

Answers

Answer 1

Answer:

a) x = 40 t , y = 39 t ,  z = 6 + 32 t - 16 t ²,   b)     x = 80 feet ,  y = 78 feet , the ball came into the field  

Explanation:

a) This is a projectile launch exercise, where in the x and y axes there is no acceleration and in the z axis the acceleration of the acceleration of gravity, let's write the equations of motion in each axis

Since the cast is in the center of the field, let's place the coordinate system

          x₀ = 0

          y₀ = 0

          z₀ = 6 feet

x-axis (towards end zone,  GOAL zone)

         x = xo + v₀ₓ t

        x = 40 t

y-axis (field width)

        y = y₀ + [tex]v_{oy}[/tex] t

        y = 39 t

z axis (vertical)

        z = z₀ + v_{oz} t - ½ g t²

        z = 6 + 32 t - ½ 32 t²

        z = 6 + 32 t - 16 t ²

b) The player catches the ball at the same height as it came out, so we can find the time it takes to arrive

          z = 6

          6 = 6 + 32 t - 16 t²

          (t - 2)t  = 0

           t=0 s

           t= 2 s

The ball position

          x = 40 2

          x = 80 feet

           

          y = 39 2

          y = 78 feet

the dimensions of the field from the coordinate system (center of the field) are

             x_total = 150 feet

             y _total = 80 feet

so we can see that the ball came into the field


Related Questions

Consider two current-carrying circular loops. Both are made from one strand of wire and both carry the same current, but one has twice the radius of the other. If the magnetic field strength at the center of the smaller loop is B, what is the magnetic field strength at the center of the larger loop

Answers

Explanation:

The magnetic field at the center of a current-carrying circular loop is given by :

[tex]B=\dfrac{\mu_o I}{2r}[/tex]

Where, I is current and r is radius of loop

We have, two current-carrying circular loops. Both are made from one strand of wire and both carry the same current, but one has twice the radius of the other.

For smaller loop, the magnetic field is B (with radius r)

For larger loop, let the magnetic field be B' (with radius r', r'=2r). So,

[tex]B'=\dfrac{\mu_o I}{2r'}\\\\B'=\dfrac{\mu_o I}{2(2r)}\\\\B'=\dfrac{1}{2}\times \dfrac{\mu_o I}{2r}\\\\B'=\dfrac{1}{2}B[/tex]

Hence, the magnetic field strength at the center of the larger loop is half of the magnetic field strength at the center of the smaller loop.

If the force from the tibia on the femur illustrated below was 1000 N acting at 30° to the femur,
what are the components of this force Fs and Fl:
1000 N
F
300

Answers

Answer:

tibia would be 100N x 300

Explanation:

10. The electron dot diagram for the element Ne would have ​

Answers

Answer:

2,8

Explanation:

The first electron shell would have 2 electrons, the second shell would have 8 electrons. This is because Neon has a relative charge of 10.

The table represents the speed of a car in a northern direction over several seconds. Column 1 would be on the x-axis, and Column 2 would be on the y-axis. Which best lists the titles of each column? Column 1 0 2. 4 6 8 10 Column 2 5 10 15 20 25 30 O Column 1 should be titled "Time," and Column 2 should be titled "Velocity." O Column 1 should be titled "Velocity," and Column 2 should be titled "Time." O Column 1 should be titled "Time," and Column 2 should be titled "Acceleration." O Column 1 should be titled "Acceleration," and Column 2 should be titled "Time."​

Answers

Answer is A hope this helps luv

Answer:

Column 1 should be titled “Time,” and Column 2 should be titled “Velocity.”

Explanation:

Are renewable resources always renewable, or can they become non-renewable

Answers

Answer:

Can become non-renewable but it depends on the object

Explanation:

Answer:

Renewable resources are so abundant or are replaced so rapidly that, for all practical purposes, they can't run out. Fossil fuels are the most commonly used non-renewable resources

Explanation:

Hope this helps (:

need help ASAP. please and thank you ​

Answers

I believe the correct answer is 9

What is the frequency (n, in Hz) of the photons emitted by a He-Ne laser with a wavelength (l) of 632.8 nm

Answers

Answer:

4.741 × 10¹⁴ Hz

Explanation:

Step 1: Given data

Wavelength of the He-Ne laser (l): 632.8 nmFrequency of the He-Ne laser (n): ?Speed of light (c): 3.000 × 10⁸ m/s

Step 2: Convert "l" to meters

We will use the conversion factor 1 m = 10⁹ nm.

632.8 nm × (1 m / 10⁹ nm) = 6.328 × 10⁻⁷ m

Step 3: Calculate the frequency of the He-Ne laser

We will use the following expression.

c = l × n

n = c / l

n = (3.000 × 10⁸ m/s) / (6.328 × 10⁻⁷ m)

n = 4.741 × 10¹⁴ s⁻¹ = 4.741 × 10¹⁴ Hz

An area that has been re-colonized after an environmental disturbance has undergone ____________. Group of answer choices Stratification Zonation Primary Succession Secondary Succession

Answers

Answer:

Secondary succession

Explanation:

Secondary succession is one of the two major types of ecological successions (the other being primary succession). Succession, generally, is characterized by the series of changes that occurs to an ecological community within a period of time.

However, secondary succession occurs when an already colonized area (with soil formed) becomes disturbed by environmental disasters or occurrences, leading to the recolonization of the area by certain organisms. Therefore, an area that has been re-colonized after an environmental disturbance has undergone SECONDARY SUCCESSION.

After a wave passes through a medium, particles in the medium
are permanently displaced in a direction opposite to the direction of the wave
remain in the new location
are moved along with the wave
return to the original position

Answers

Answer:

D. Return to the original position

Explanation:

I took the test

I need helpppppppppppppppppp!

Answers

Answer:

i think its B

Explanation:

but check it before do it  

Answer:

A

Explanation:

Hope it helps I tried looking for think I found it hit the heart pls

Question 5 of 10
Two hockey pucks, each with a mass of 0.15 kg, slide across the ice and
collide. Before the collision, puck 1 is moving 14 m/s to the west and puck 2
is moving 10 m/s to the east. After the collision, puck 1 is moving at 10 m/s
to the east. What is the velocity of puck 2?
A. 14 m/s east
B. 10 m/s west
C. 10 m/s east
D. 14 m/s west

Answers

Answer: D. 14 m/s west

Explanation:

I just did it on A p e x

please answer please please


Physics ​

Answers

Answer:

  about -1.26 m/s²

Explanation:

The acceleration can be found from the formula ...

  a = (v2² -v1²)/(2d)

Here, we have the initial velocity v1=23 m/s, the final velocity v2=0, and teh distance d=210 m. Using the formula, we find the acceleration to be ...

 a = (0 -23²)/2(210) ≈ -1.2595 . . . m/s²

The barren-ground caribou shown below is a large herbivore that lives in a subarctic climate near Yellowknife, Canada. Which of these is NOT an adaptation found in caribou?
A. Caribou have wide feet to help them avoid sinking into deep snow.
B. Caribou can digest a diet of grasses, twigs, and mushrooms.
C. Caribou can hold their breath for up to nine minutes underwater.
D. Caribou migrate between a summer location with abundant food and a winter location where conditions (weather, food, snow cover) are more favorable.

Answers

Answer:

C - Caribou can hold their breath for up to nine minutes

Explanation:

The other three are true.

The statement which is NOT an adaptation found in Caribou is:

C. Caribou can hold their breath for up to nine minutes underwater.

According to the given question, we need to find the adaptation which is false from the answer choices about the large herbivore called Caribou.

As a result of this, the adaptation which cannot be found in Caribou is the statement that Caribou can hold their breath underwater for up to nine minutes which is false.

Therefore, the correct answer is option C

Read more here:

https://brainly.com/question/15996015

PLEASE HLEP ME ASAP

Tom, a 13 year old boy, wants to train for a 5k Fun Run that his school is organizing. What area of fitness should Tom focus on? What activities should he do to improve this area?

Answers

Answer:

cardiovascular endurance

Explanation:

In order for Tom to successfully complete the marathon, he should focus on being able to maintain a constant pace without tiring easily.

Perception of color is determined by the wavelength of light that an object reflects
Please select the best answer from the choices provided
T
Or
F

Answers

Answer:

True

Explanation:

hope I could help :)

Answer:

true

Explanation:

i know my stuff

A placekicker kicks a football at and angle of 40.0 degrees and the initial speed of the ball is 22 m/s. Ignoring air resistance, determine the maximum height that the ball attains.

Answers

Answer:

10.18m

Explanation:

in this problem, we are expected to solve for the maximum height of a projectile (the ball)

Firstly, the expression for maximum height is

h = u ^2 *sin ^2 θ /2 g

Given data

initial velocity u=22m/s

angle of projection, θ= 40degrees

substituting into the expression we have

h = 22^2 *sin (40)^2 /2 *9.81

h = 484*0.413 /19.62

h =199.892 /19.62

h=10.18m

The maximum height is 10.18m

The maximum height attains by ball is 48.64 meter.

The maximum height is given by using formula,

                  [tex]h=\frac{u^{2}*sin2\theta }{g}[/tex]

Where u is initial velocity, and value of [tex]g=9.8m/s^{2}[/tex]

Given that,   [tex]u=22m/s,\theta=40,g=9.8m/s^{2}[/tex]

Substituting above values in formula.

             [tex]h=\frac{(22)^{2}*sin80 }{9.8} =\frac{484*0.98}{9.8} =48.64m[/tex]

Hence, the maximum height attains by ball is 48.64 meter.

Learn more:

https://brainly.com/question/20689870

Calculate the maximum energy that a 3-MeV alpha particle can transfer to an electron in a single collision.

Answers

Answer:

The maximum energy that can be transferred to an electron in a single collision of alpha particle is 1.63 keV

Explanation:

let mass of electron, Me = 1

let mass of proton, Mp = 1836Me = 1836

let mass of alpha particle, Ma = 4Mp = 7344

The maximum energy that can be transferred to an electron in a single collision is given by;

[tex]Q_{max} = \frac{4mME}{(M+m)^2}\\\\Q_\alpha_{max} = \frac{4(1)(7344)(3\ MeV)}{(1+7344)^2} = 0.00163 \ MeV = 1.63 \ KeV[/tex]

Therefore, the maximum energy that can be transferred to an electron in a single collision of alpha particle is 1.63 keV

When an atom gains or loses electrons, it has an electrical charge. It is known as

Answers

Answer:

ion

Explanation:

Atoms can gain or lose making them no longer neutral they become charged and it is called ion.

A ball is dropped from a 19m high cliff. The acceleration on the ball was 9.8m/s². What was the ball's final velocity before hitting the ground?

Answers

Answer:

19.3 m/s

Explanation:

Take down to be positive.  Given:

Δy = 19 m

v₀ = 0 m/s

a = 9.8 m/s²

Find: v

v² = v₀² + 2aΔy

v² = (0 m/s)² + 2 (9.8 m/s²) (19 m)

v = 19.3 m/s

Which of the following fields can only exist in one direction?

Answers

It’s B hope it helps

A vector is 9.55m long and points in a -48.0 degree direction. find the x component​

Answers

Answer:

x=6.39 m

Explanation:

Rectangular Components of a Vector

Vectors can be expressed in several forms, including the magnitude-angle form, and the rectangular-coordinates form.

If the magnitude r and angle β are given, we can find the rectangular coordinates (x,y) as follows:

[tex]x=r\cos\beta[/tex]

[tex]y=r\sin\beta[/tex]

The vector of the question has a magnitude of r=9.55 m and an angle β=-48°. The x-component is:

[tex]x=9.55\cdot\cos(-48^\circ)[/tex]

Using a digital calculator:

x=6.39 m

x component = 6.39y component = -7.09formulas:x = r * cos * βy = r * sin * βplug in numbers:x = 9.55 * cos (-48°)y = 9.55 * sin (-48°)

Which statement describes earthquakes?
They release energy
They are caused by reduced stress in rocks
They begin at the epicenter
The result for movement on earth’s surface

Answers

Answer:

they release energy  

Explanation:

An earthquake is the abrupt release of energy from the earth's crust that causes the earth's surface to shake . Thus , seismic waves are produced. The kind and severity of an earthquake are based on the local seismic activity . therefore the correct answer is option A.

What is the equator?

The Equator is an imaginary line passing through the middle of a globe. It is equidistant from the North Pole and the South Pole, Its is a horizontal line residing at 0 degrees latitude .

An earthquake is the abrupt release of energy from the earth's crust that causes the earth's surface to shake . Thus, seismic waves are produced. The kind and severity of an earthquake are based on the local seismic activity .

Thus, the correct answer is option A .  

To learn more about the equator here , refer to the link given below ;

brainly.com/question/24203207

#SPJ6


Select the correct answer from each drop-down menu.
Rocky metallic objects found between the orbits of Mars and Jupiter are(drop down). The largest known of these is(drop down).

Answers

Answer:

Blank 1 (asteroids)

Blank 2 (Ceres)

Explanation:

Rocky metallic objects found between the orbits of Mars and Jupiter are asteroids The largest known of these is ceres.

What are asteroids?

Asteroids are stony elements that circle the Sun. Although asteroids circle the Sun in the same way as planets, they are considerably smaller.]

A dwarf planet located between Mars and Jupiter in the asteroid belt. Ceres was the first asteroid discovered, it was originally classed as a planet,

Rocky metallic objects found between the orbits of Mars and Jupiter are asteroids The largest known of these is ceres.

The correct option from the drop-down menu is asteroids and ceres.

To learn more about the asteroids refer to the link;

https://brainly.com/question/19161842

A force of 50n is applied to an object at an angle of 50 degrees measured relative to the horizontal. Determine the horizontal and vertical components of the applied force?

Answers

Answer:

Fx = 32.14 [N]

Fy  = 38.3 [N]

Explanation:

To solve this problem we must decompose the force vector, for this we will use the angle of 50 degrees measured from the horizontal component.

F = 50 [N]

Fx = 50*cos(50) = 32.14 [N]

Fy = 50*sin(50) = 38.3 [N]

We can verify this result using the Pythagorean theorem.

[tex]F = \sqrt{(32.14)^{2}+ (38.3)^{2}} \\F = 50 [N][/tex]

If I kick a ball off the top of a mountain cliff, will it take longer to hit the ground than if I just drop it? Explain your answer. Your answer:

Answers

Answer:

they will drop at the same time

Explanation:

projectile motion consists of two components, horizontal and vertical, which are independent of one another. That means that if you drop a ball and kick another one straight out, they will both hit the ground at the same time so long as they have the same initial drop height .

Please help me if you know physics

Answers

Answer:

  19.  down

  20.  True

Explanation:

The examples I saw were projectiles launched at different angles and speeds. In each case, the only acceleration was ...

  19:  down

  20:  due to gravity (true)

What is the correct order of organization from smallest to largest?

a.Tissues, cells, organs, organism, organ system
b.Cells, organs, tissues, organ system, organism
c.Organs, tissues, organ system, cells, organism
d.Cells, tissues, organs, organ system, organism

Answers

Answer:

D

Explanation:

Cells are the smallest unit of organizaiton, followed by tissues, organs, organ systems, and then organisms themselves.

Organ system that is responsible for breaking down food

a.Digestive
b.Respiratory
c.Circulatory
d.Nervous

Answers

Answer:

A. Digestive

Explanation:

Answer:

digestive system

Explanation:

since the digestive system secretes enzymes like amylase,lipase etc. required by the body for the proper breakdown of food.

an airplane travels down a Runway at 1500 m in 17s what is the average speed

Answers

Answer:

88.23 m/s

Explanation: The equation for speed is s=d/t so in other words, speed equals distance over time so the distance is 1500 and the time is 17 seconds so you just devide 1500 by 17 and you get the speed. Remember to include your unit m/s after your answer

2
A crane has an arm to which is attached a frictionless pulley. A cable passes over the pulley and
supports a load of 10 kN as shown.
frictionless pulley
104N
30
30°
crane arm
load
10 KN
The crane arm exerts a force F on the pulley.
What is the value of F?
C
8.7 KN
10 KN
D
A
17 kN
B
5.0 KN

Answers

Answer:

17kN

Explanation:

The force of 10 kN in the cable and the load of 10 kN both have a component along the crane arm.

The force F exerted by the crane arm on the pulley is the sum of these 2 components.

Component of force in cable along the crane arm = 10 cos 30°

Component of load along the crane arm = 10 cos 30°

Considering the forces on the pulley,

F = 10 cos 30° + 10 cos 30°

Force F = 17.32 kN = 17 kN

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