Answer to Question #214618 in Civil and Environmental Engineering for syra

Question

A ball rolls of the edge of a table top 1.0 m high and strikes the floor at a point 15m horizontally away from the edge of the table. Find (a) the time of flight, (b) the initial velocity, and (c) the magnitude and direction of the velocity of the ball just before it strikes the floor

Answer 1

Part a

$s=\frac{1}{2}gt^2\\ t= \sqrt{\frac{2s}{g}}\\ t= \sqrt{\frac{2*1}{9.81}}\\ t= 0.4515 s\\$

Part b

$u_x=\frac{Distance}{Time}\\ u_x=\frac{15}{0.4515}\\ u_x=33.22 \\ u_y=gt\\ u_y=9.81*0.4515\\ u_y=4.4292\\ v= \sqrt{33.22^2+4.4292^2}\\ v=33.5139 m/s$

Part c

$\theta = \tan ^{-1}(\frac{4.4292}{33.22})\\ \theta = 7.59^0$