Page 47 - Schaum's Outline of Theory and Problems of Applied Physics

32 MOTION IN A STRAIGHT LINE [CHAP. 3

SOLVED PROBLEM 3.1
A ship travels 9 km in 45 min. What is its speed in kilometers per hour?
3
Since 45 min = h,
4
s 9km
v = = 3 = 12 km/h
t h
4

SOLVED PROBLEM 3.2
8
The velocity of light is 3.0 × 10 m/s. How long does it take light to reach the earth from the sun, which
11
is 1.5 × 10 m away?
11
s 1.5 × 10 m
t = = = 500 s = 8.3 min
8
v 3.0 × 10 m/s
SOLVED PROBLEM 3.3

You are standing 100 m north of your car when an alligator appears 20 m north of you and begins to run
toward you at 8 m/s. At the same moment you start to run toward your car at 5 m/s. (a) Will you reach
the car before the alligator overtakes you? (b) If not, how far from your car does the alligator have lunch?
(a) You would need

s 1 100 m
t 1 = = = 20 s
v 1 5 m/s
to reach your car, but the alligator would need only
s 2 120 m
t 2 = = = 15 s
v 2 8 m/s
Hence the alligator will overtake you before you get to the car. Too bad.
(b) If the alligator catches up with you in the time t at the distance d from your car, you will have gone 100 m − d
at the velocity v 1 and the alligator will have gone 120 m − d at the velocity v 2 . Thus there are two formulas
for t,

100 m − d 120 m − d
t = =
v 1 v 2
100 m − d 120 m − d
and so =
5 m/s 8 m/s
Solving for the distance d gives

(8 m/s)(100 m − d) = (5 m/s)(120 m − d)
800 m − 8d = 600 m − 5d
3d = 200 m
d = 67 m

SOLVED PROBLEM 3.4
A car travels 270 km in 4.5 h. (a) What is its average velocity? (b) How far will it go in 7.0 h at this
average velocity? (c) How long will it take to travel 300 km at this average velocity?