A ball is launched directly in the air at a speed of 40 feet per second from a platform located 10 feet in the air. The motion of the ball can be modeled using the function f (t) = -16t2+40t+10, where t is the time in seconds and f (t) is the height of the ball. When, in seconds, will the ball hit the ground? Write your answer to the nearest hundredth of a second. Do not include units in your answer.

Question

Physics

Gavyn Gibson

31 December, 01:18

A ball is launched directly in the air at a speed of 40 feet per second from a platform located 10 feet in the air. The motion of the ball can be modeled using the function f (t) = -16t2+40t+10, where t is the time in seconds and f (t) is the height of the ball. When, in seconds, will the ball hit the ground? Write your answer to the nearest hundredth of a second. Do not include units in your answer.

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Answers (1)

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Savanna · Answer 1

The ball will hit the ground in 2.73 s

Explanation:

Hi there!

f (t) is the height of the ball at time "t". We need to find the value of "t" for which f (t) = 0.

f (t) = 0 Then:

-16 · t² + 40 · t + 10 = 0

Solving the quadratic equation using the quadratic formula (a = - 16, b = 40, c = 10):

t = - 0.23 s and t = 2.72 s

Since time can't be negative, be discard that value.

The ball will hit the ground in 2.73 s.

Have a nice day!