Question

A ball is rolled horizontally off the edge of a 125 cm tall table. The ball lands 2.0 m away from the base of the table. How fast is the ball moving when it hits the floor. (This is not just the vertical final velocity).

Answer 1

Answer on Question #48281, Physics, Mechanics | Kinematics | Dynamics

Question:

A ball is rolled horizontally off the edge of a 125 cm tall table. The ball lands 2.0 m away from the base of the table. How fast is the ball moving when it hits the floor. (This is not just the vertical final velocity).

Answer:

Coordinates of the ball equals:

$$x = v_x t$$ $$y = h_0 - \frac{g t^2}{2}$$

The ball hits the floor if $y=0$:

$$y = 0 \Rightarrow t = \sqrt{\frac{2h}{g}}$$

Therefore components of velocity equal:

$$v_x = \frac{x}{t}$$ $$v_y = g t$$

Total velocity:

$$v = \sqrt{v_x^2 + v_y^2} = \sqrt{\frac{x^2 g}{2h} + 2 g h} = 6.34 \frac{m}{s}$$

Answer: $6.34 \frac{m}{s}$

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