v = v + v
DR
BR
DB
v = v + v
DR
BR
DB
v = 55 mph + 45 mph
DR
v = 100 mph
DR
v = 100 mph in the direction in which the bus is traveling
DR
You already know all the concepts you need to know to solve relative velocity problems (you
know what velocity is and you know how to do vector addition) so the best we can do here is to
provide you with some more worked examples. We’ve just addressed the easiest kind of relative
velocity problem, the kind in which all the velocities are in one and the same direction. The
second easiest kind is the kind in which the two velocities to be added are in opposite directions.
Example 11-1
A bus is traveling along a straight highway at a constant 55 mph. A person sitting at
rest on the bus fires a dart gun that has a muzzle velocity of 45 mph straight
backward, (toward the back of the bus). Find the velocity of the dart, relative to the
road, as it leaves the gun.
Again defining:
v to be the velocity of the bus relative to the road,
BR
v to be the velocity of the dart relative to the bus, and
DB
v to be the velocity of the dart relative to the road, and
DR
defining the forward direction to be the positive direction; we have
v
BR
FORWARD
v
Positive Direction
DR
|v |
DB
v = v + v
DR
BR
DB
v = v − |v |
DR
BR
DB
v = 55 mph − 45 mph
DR
v = 10 mph
DR
v = 10 mph in the direction in which the bus is traveling
DR
63