Question

A ball rolls off the edge of a 2 m high table with an initial velocity of 10 m/s.

A.How far from the edge of the table will the ball land?








B. Determine the ball’s velocity just before it strikes the floor?

Answer 1

A) Let's first find the time that the ball takes to reach the floor:

$$y=\dfrac{1}{2}gt^2,$$ $$t=\sqrt{\dfrac{2y}{g}}=\sqrt{\dfrac{2\cdot2\ m}{9.8\ \dfrac{m}{s^2}}}=0.64\ s.$$

Finally, we can find the distance from the edge of the table to the point where the ball lands:

$$x=v_{0}t=10\ \dfrac{m}{s}\cdot0.64\ s=6.4\ m.$$

B) Let's first find final vertical velocity of the ball just before it strikes the floor:

$$v_y=-gt=-9.8\ \dfrac{m}{s^2}\cdot0.64\ s=-6.27\ \dfrac{m}{s}.$$

Finally, we can find the ball’s velocity just before it strikes the floor from the Pythagorean theorem:

$$v=\sqrt{v_x^2+v_y^2}=\sqrt{(10\ \dfrac{m}{s})^2+(-6.27\ \dfrac{m}{s})^2}=11.8\ \dfrac{m}{s}.$$