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Dropping a basketball from a 5 story building and its velocity.?

Say you drop a basketball from the top of a five story building onto a sidewalk 70 feet below.

Q1. What is the initial velocity of the basketball?

Q2. Determine a function for the height of the basketball t seconds after it's released.

Q3. How long will the basket ball be in the air before it hits the ground?

Please help me with this problem. Thank you.

Q1. The ball is just dropped so the motion is all vertical

and the initial velocity (vertical velocity) of the ball is 0 ft/s

Q2. The building is 70 feet tall

s = v(i)t + (1/2)at² where t is the time since release

a = g = 32.2 ft/s² ... (taking down as the positive direction)

so s = 0 + (1/2) * 32.2t²

s = 16.1t²

h(t) = 70 - 16.1t² where h(t) is the height of the ball after t seconds

Q3. when the ball hits the ground h(t) = 0

so 70 - 16.1t² = 0

16.1t² = 70

t = √(70/16.1)

t = 2.1 s (to 2 sig figs)

so the ball will be in the air for 2.1 s b4 it hits the ground

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