an equation that could be used to determine the time, t, in seconds, for the ball to reach the ground. Assume ground level is at a height of 0 ft.

Question

The height, h, of an object that is thrown upwards into the air can be represented as h = 0.5 at 2 + v 0 t + h 0, where a represents the acceleration due to gravity (– 32ft

s

² ), v ₀ represents the initial velocity, in feet per second, h ₀ represents the initial height of the object, in feet, and t represents time, in seconds. 

Part A: 

A ball thrown upwards from the top of a 64–ft high building with an initial velocity of 48ft

s

. Write an equation that could be used to determine the time, t, in seconds, for the ball to reach the ground. Assume ground level is at a height of 0 ft. 

Part B: 

Determine the time, t, in seconds, that takes the ball to reach the ground and explain how you determined your answer.

Answer 1

Part A:

They give you the starting equation:

h = 0.5at² + v₀t + h₀, and they tell you that a = -32, that h₀ = 64, and that v₀ = 48. If we plug these three numbers in, we will have the equation we're after.

h = 0.5(-32)t² + 48t + 64

h = -16t² + 48t + 64

Part B:

Reaching the ground would mean that h = 0. Factor this quadratic to solve for t.

0 = -16t² + 48t + 64

0 = -16(t² - 3t - 4)

0 = -16(t - 4)(t + 1)

t - 4 = 0 means t = 4

t + 1 = 0 means t = -1, but this doesn't make any sense in our real-world problem.

Therefore, the solution is 4 seconds.

Answer 2

The time t required is the zero of -16t² + 48t + 64 = 0 which factors easily.