Question

1.   A ball is dropped from rest of a cliff of height 100 m. Assuming gravity accelerates masses uniformly on Earth's surface at g = 9.8 m/s², how fast is the ball going when it hits the ground? How long does it take to hit the ground?

Answer 1

Let's first find the time that the ball takes to reach the ground:

$$y=\dfrac{1}{2}gt^2,$$ $$t=\sqrt{\dfrac{2y}{g}}=\sqrt{\dfrac{2\cdot100\ m}{9.8\ \dfrac{m}{s^2}}}=4.52\ s.$$

Then, we can find the vertical velocity of the ball when it hits the ground:

$$v=v_0-gt=0-9.8\ \dfrac{m}{s^2}\cdot4.52\ s=-44.3\ \dfrac{m}{s}.$$

The sign minus means that the velocity of the ball directed downward.