Velocity (Vertical Component)

Question

A ball is thrown from a rooftop with an initial downward velocity of magnitude v_o = 1.3 m/s. The rooftop is a distance above the ground, h = 42 m. In this problem use a coordinate system in which upwards is positive.

Find the vertical component of the velocity, in meters per second, with which the ball hits the ground.

Answer 1

You are given the initial velocity and height, and since you are given that the ball is dropping you have

s=y-y_o= -42m and v_o =-1.3m/s and a=-9.8m/s² (free fall acceleration).

Thus we can find the v=final velocity by using the equation

v² = v_o² +2as = (-1.3)²+2(-9.8)(-42)=1.69+205.8 =207.49 ⇒ v=-14.4 m/s

Negative velocity makes sense since both initial velocity and acceleration are in the downward direction.