Jon is hitting baseballs. When he tosses the ball into the air, his hand is 5 feet above the ground. He hits the ball when is falls back to a height of 4 feet. The height of the ball is given by h(t)=5+25t-16t^2, where t is the time in seconds.

a) How much time will pass before Jon hits the ball? (round to the nearest tenth of a second)
b) What is the time in which the maximum height the ball attains? ( to the nearest hundredth of a second)

Answer: A= 1.60 sec

And I am not sure if B is correct, but I got 14.77 ft.

Step-by-step explanation:

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have Jon who is hitting baseballs. When he tosses the ball into the air, his hand is 5 feet above the ground. He hits the ball when is falls back to a height of 4 feet. The height of the ball is given by -

h(t) = 5 + 25t - 16t²

where [t] is the time in seconds.

[A] -

At h = 4ft, we can write -

4 = 5 + 25t - 16t²

- 16t² + 25t + 1 = 0

On solving, we get -

t = 1.602 seconds

[B] -

We have -

h(t) = 5 + 25t - 16t²

For maximum height -

dh/dt = 0

d/dt(5 + 25t - 16t²) = 0

0 + 25 - 32t = 0

32t = 25

t = 25/32

t = 0.79 seconds

Therefore -

To solve more questions on Equation Modelling, visit the link below -

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