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

Question

, 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.

Answer 1

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.

Answer 2

What is the height of the ball

Answer 3

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.

Answer 4

the answer should be in feet