Question

You are standing on the roof of a 60 foot tall building. You throw a ball upward with an initial velocity of 100 feet per second which then falls to the ground below. 1) Determine the maximum height of the ball2) Determine the ball's final velocity when it strikes the ground 3) Determine the time required to reach its maximum height AND the time till it strikes the ground below. 4) Use Desmos and graph the function Extra Credit: Determine the initial velocity required for the object to have a maximum height of 1000 feet

Answer 1

The height of the building is 60 foot

The initial velocity = 100 feet per second

Using the equation of motion

V^2 = U^2 - 2gH

The negative sign indicates that the ball is moving against the gravity, and also the ball is moving upward while gravity is acting downward

Where V = final velocity

U = initial velocity

A = acceleration

s = height

Determine the maximum height?

The final velocity is zero

Since, the final velocity is zero, the equation becomes

0^2 = U^2 - 2gH

0 = U^2 - 2gH

-U^2 = -2gH

U^2 = 2gH

U = 100 feet per second

g = 32.80 feet per second square

100^2 = 2 x 32.80 x H

10000 = 65.6 x H

10000 = 65.6 H

Divide both sides by 65.6

10000/65.6 = 65.6H/65.6

H = 10000/65.6

H = 152.44 foot

Since, the person is standing on the roof of a 60 foot tall building

Then, the maximum height of the ball is

Hmax = 152.44 + 60

Hmax = 212. 44 foot