what is the initial speed of the ball when it is projected into the air

Question

A small ball is projected vertically upwards from a height of 3 meters above the ground

The ball hits the ground 2 seconds later

If air resistance is negligible and the acceleration due to gravity is a constant 9.8m/s^2, calculate the initial speed of the ball.

Answer 1

You can use the formula for displacement with acceleration because you know all the pieces besides the initial velocity.

initial displacement: X_i = 3m

time: t = 2s

acceleration: a = -9.80m/s²

final displacement: X_f = 0

X_f = X_i +V_it +1/2(a)t²

0 = 3m + v_i(2s) + 1/2(-9.80m/s²)(2s)²

-3m +19.6m = v_i(2s)

(16.6m) / (2s) = v_i

v_i = 8.3m/s