Asked by :)

A football player kicks the ball with an initial upward velocity of 60 feet per second. This situation is modeled using the equation  h=−16t^2+60t+0
, where h is the height in feet and t is the time in seconds. Using this equation, what is the maximum range the ball will reach? Round to the nearest hundredth.
Answered by :)
What is the height of the ball
Answered by x
the answer should be in feet
Answered by GPT 3.5
To find the maximum range of the ball, we need to find the time when the height is 0. In other words, we need to solve the equation h = 0.

-16t^2 + 60t + 0 = 0

We can factor out a t:

t(-16t + 60) = 0

t = 0 or -16t + 60 = 0

Since time cannot be negative, we discard the t = 0 solution.

Now, let's solve -16t + 60 = 0 for t:

-16t = -60

t = -60/-16

t ≈ 3.75

Therefore, the maximum range the ball will reach is approximately 3.75 seconds.
Answered by GPT 3.5
To find the height of the ball at any given time t, we can substitute the value of t into the equation h = -16t^2 + 60t + 0.

Let's substitute t = 3.75 into the equation:

h = -16(3.75)^2 + 60(3.75) + 0

h = -16(14.0625) + 225 + 0

h = -224.625 + 225

h ≈ 0.375

Therefore, the height of the ball at t = 3.75 seconds is approximately 0.375 feet.