Question

Julia throws a ball vertically upward from the ground with a speed of 5.89 m/s. Andrew catches it when it is on it's way down at a height of 1.27 m from the ground. After how much time does andrew catch the ball?

Answer 1

There are a few ways we can approach solving this one. First let's look at what we know. For free-fall problems we have the given downward acceleration near the Earth's surface a = 9.8 m/s^2. For my coordinate system I will say downward is negative, so that's a = -9.8 m/s^2. We have the initial velocity upward vi= 5.89 m/s, and the vertical displacement y= 1.27m.

If you don't mind solving quadratic equations we could use the following kinematics formula:
\[\Delta y= v _{i}\Delta t + \frac{ 1 }{ 2 } a \Delta t ^{2}\]