Question

A girl throws a ball vertically at 10 m/s from a roof of a building 20 m high.
(a.) How long will it take the ball to reach the ground?
(b.) What will its velocity be when it strikes the ground?

Answer 1

The earth has a gravitational acceleration of -10m/s^2. You need know some cinematic formulas. First, \[x _{f}=x_{i}+v _{i}t+\frac{ 1 }{ 2 }at ^{2}\](xf: final position; xi: initial position, vi: initial velocity, t:time, a:acceleration)

You solve this formula for "t" using the quadratic formula.\[t=\frac{ -v _{i} \pm \sqrt{v _{i }^{2}-4(a)(x _{i}-x _{f})} }{ 2a }\]Finally you plug in your numbers. I don't have a calculator, so you will have to compute yourself:\[t=\frac{ -(10\frac{ m }{ s }) \pm \sqrt{(10\frac{ m }{ s })^{2}-4(-10\frac{ m }{ s ^{2} })(20m-0m)} }{ 2(-10\frac{ m }{ s ^{2} }) }\]It may seem intimidating, but you just need to plug in the numbers