Question

Please help

Spencer hits a tennis ball past his opponent. The height of the tennis ball, in feet, is modeled by the equation h(t) = –0.075t2 + 0.6t + 2.5, where t is the time since the tennis ball was hit, measured in seconds. How long does it take for the ball to reach the ground?

A. 0.82 seconds
B. 11.02 seconds
C. 47.02 seconds
D. 1.11 seconds
thank you

Answer 1

11.02 seconds

Explanation:

Given : The height of the tennis ball, in feet, is modeled by the equation
`h(t) = -0.075t^2 + 0.6t + 2.5` where t is the time since the tennis ball was hit, measured in seconds.

To Find: How long does it take for the ball to reach the ground?

Solution:

`h(t) = -0.075t^2 + 0.6t + 2.5`

Now we are supposed to find How long does it take for the ball to reach the ground , i.e. h = 0

`0 = -0.075t^2 + 0.6t + 2.5`

`-0.075t^2 + 0.6t + 2.5=0`

`t=11.02,-3.02`

So, time cannot be negative

So, it take 11.02 seconds for the ball to reach the ground

Answer 2

Hence, option: B is correct (11.02 seconds)

Explanation:

Spencer hits a tennis ball past his opponent. The height of the tennis ball, in feet, is modeled by the equation h(t) = –0.075t2 + 0.6t + 2.5, where t is the time since the tennis ball was hit, measured in seconds.

Now we are asked:

How long does it take for the ball to reach the ground?

i.e. we have to find the value of t such that height is zero i.e. h(t)=0.

`-0.075t2+0.6t+2.5=0`

or
`0.075t^2-0.6t-2.5=0`

i.e. we need to find the roots of the above quadratic equation.

on solving the equation we get two roots as:

t≈ -3.02377 and t≈11.0238

As time can't be negative; hence we will consider the value of t as t≈11.0238.

Hence it takes 11.02 seconds for the ball to reach the ground.

Hence option B is correct (11.02 seconds).