Page 59 - Schaum's Outline of Theory and Problems of Applied Physics

44 MOTION IN A VERTICAL PLANE [CHAP. 4

Fig. 4-3

(a) The horizontal velocity of the wheel does not affect its vertical motion (Fig. 4-3). The wheel therefore reaches
the ground at the same time as a wheel dropped from rest at an altitude of 1500 m, which is

2h (2)(1500 m)
t = = = 17.5s
g 9.8 m/s 2
(b) The horizontal component of velocity of the wheel is

km 1000 m/km
v x = 500 = 139 m/s
h 3600 s/h
In t = 17.5 s the wheel will travel a horizontal distance of
x = v x t = (139 m/s)(17.5s) = 2433 m = 2.43 km
(c) The final velocity of the wheel has the horizontal component v x = 139 m/s and the vertical component
2
v y = gt = (9.8 m/s )(17.5s) = 172 m/s
Hence the final velocity is

2 2 2 2
v = v + v = (139 m/s) + (172 m/s) = 221 m/s
y
x
SOLVED PROBLEM 4.10
A football is thrown with a velocity of 10 m/s at an angle of 30 above the horizontal. (a)How faraway
◦
should its intended receiver be? (b) What will the time of flight be?
v 2 (10 m/s) 2
◦
(a) R = 0 sin 2θ = (sin 60 ) = 8.8m
g 9.8 m/s
◦
2v 0 sin θ (2)(10 m/s)(sin 30 )
(b) T = = = 1.02 s
g 9.8 m/s 2
SOLVED PROBLEM 4.11
An air rifle is fired at an angle of 60 above the horizontal. (a) If the pellet’s initial velocity is 40 ft/s,
◦
how far does it go? (b) What is its time of flight?
◦
(a) Here 2θ = 120 . Hence
v 2 0 (40 ft/s) 2
◦
R = sin 2θ = 2 (sin 120 ) = 43 ft
g 32 ft/s
2v 0 sin θ (2)(40 ft/s)(sin 60 )
◦
(b) T = = = 2.17 s
g 32 ft/s 2