Page 58 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 4] MOTION IN A VERTICAL PLANE 43

Fig. 4-1

SOLVED PROBLEM 4.8

A ball is thrown horizontally from a cliff at 8 m/s. (a) How fast is it moving 2 s later? (b) In what direction
is it moving?

(a) The ball’s velocity after 2 s has the horizontal component v x = 8 m/s and the vertical component
2
v y = gt = (9.8 m/s )(2s) = 19.6 m/s
Hence the magnitude of its final velocity is

2 2 2 2
v = v + v = (8 m/s) + (19.6 m/s) = 21.2 m/s
x y
(b) From Fig. 4-2 we see that
v y
tan θ =
v x
where θ is the angle of the ball’s velocity below the horizontal. The angle θ is accordingly
19.6 m/s
v y
θ = tan −1 = tan −1 = 68 ◦
v x 8 m/s

Fig. 4-2

SOLVED PROBLEM 4.9
An airplane is in level flight at a velocity of 500 km/h and an altitude of 1500 m when a wheel falls off.
(a) How long does the wheel take to reach the ground? (b) What horizontal distance will the wheel travel
before it strikes the ground? (c) What will the wheel’s velocity be when it strikes the ground?