A visitor is staying in a tent that is 11 kilometers west of the closest point on a shoreline to a coral reef. The coral reef is 3 kilometers due south of the shoreline. The visitor plans to travel from the tent to the coral reef by running and swimming. If the visitor runs at a rate of 7 kmph and swims at a rate of 2 kmph, how far should the visitor run to minimize the time it takes to reach the coral reef

Answer:

The centripetal acceleration of a point on the outer tip of a blade is 1.097 m/s²

Explanation:

Given;

length of the fan blade, r = 0.25 m

angular speed = 20 rpm

The angular speed in rad/s is given as;

[tex]\omega = \frac{20 \ rev}{ \ \ \min} \ \times \ \frac{2\pi}{1 \ rev} \ \times \ \frac{1 \ \min}{60s} = 2.095 \ rad/s \\\\[/tex]

The centripetal acceleration of a point on the outer tip of a blade is given as;

[tex]\alpha_c = \frac{v^2}{r} = \omega ^2r[/tex]

[tex]\alpha _c = (2.095)^2(0.25)\\\\\alpha _c =1.097 \ m/s^2[/tex]

Therefore, the centripetal acceleration of a point on the outer tip of a blade is 1.097 m/s²

Answer:

Explanation:

Given

[tex]rpm = 20[/tex]

therefore,

[tex]20rpm = \frac{20*2\pi}{60}\\\\=2.1 rad/s = w[/tex]

From,

[tex]V = rw\\\\V = 0.25 * 2.1\\\\V = 0.525m/s[/tex]

Centripetal acceleration,

[tex]a_c = \frac{V^2}{r}\\\\a_c = \frac{0.525^2}{0.25}\\\\a_c = 1.1m/s^2[/tex]

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If Dominic has a brain injury, then he must have sustained a serious injury.

The brain coordinates all the activities in the body such as speech, locomotion, coordination and intelligence. This makes the brain the master point of control in the body.

Whenever there is an injury to the brain, various parts of the body could be affected. Functions such as speech, locomotion and general coordination may become largely impaired.

Therefore, if Dominic has a brain injury, then he must have sustained a serious injury.

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Answer:

τ = 5 s

Explanation:

When a vibrating body is damped. Its amplitude starts to decrease. This decrement is exponential. And it is given as follows:

[tex]X = X_{0}e^{-\frac{t}{2\tau}[/tex]

where,

τ = Time Constant = ?

X = Instantaneous value of amplitude

X₀ = Initial Value of amplitude

t = time interval = 10 s

The ratio of decrement is given as:

[tex]\frac{X}{X_0} = 36.8\% = 0.368[/tex]

therefore, using these values, we get:

[tex]\frac{X}{X_{0}} = 0.368 = e^{\frac{10\ s}{2\tau}}[/tex]

Taking natural log (ln) on both sides, we get:

[tex]ln(0.368) = \frac{10\ s}{2\tau}\\\\\tau = \frac{10\ s}{2ln(0.368)}[/tex]

τ = 5 s

The value of the time constant for the decrease in the amplitude of this oscillator is 5.

Given the following data:

To determine the value of the time constant:

Mathematically, the amplitude for damped harmonic motion is given by the formula:

[tex]X = X_o e^\frac{t}{2 \tau}[/tex]

Where:

Rearranging the formula, we have:

[tex]\frac{X}{X_o} = e^{-\frac{t}{2 \tau}}[/tex]

Substituting the given parameters into the formula, we have;

[tex]0.368 = e^\frac{-10}{2 \tau}\\\\ln(0.368) = \frac{-10}{2 \tau}\\\\-0.9997 = \frac{-10}{2 \tau}\\\\2 \tau \times -0.9997 = 10\\\\-1.9994\tau=-10\\\\\tau =\frac{-10}{-1.9994} \\\\\tau = 5.0[/tex]

Time constant = 5

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