A small ball rolls horizontally off the edge of a tabletop that is 1.23 m high. It strikes the floor at a point 1.49 m horizontally away from the edge of the table. (a) How long is the ball in the air? (b) What is its speed at the instant it leaves ?

Nov 3, 2015

$\left(a\right) . 0.5 \text{s}$

$\left(b\right) . 2.98 \text{m/s}$

Explanation:

$\left(a\right) .$

Taking the vertical component of the motion and setting the initial velocity equal to zero we get:

$s = \frac{1}{2} \text{g} {t}^{2}$

$\therefore {t}^{2} = \frac{2 s}{\text{g}} = \frac{2 \times 1.23}{9.8} = 0.251$

$\therefore t = \sqrt{0.251} = 0.5 \text{s}$

$\left(b\right) .$

The horizontal component of velocity is constant so:

$v = \frac{s}{t} = \frac{1.49}{0.5} = 2.98 \text{m/s}$