It would be odd looking at that dart from the side of the road. Relative to you it would still be
moving in the direction that the bus is traveling, tail first, at 10 mph.
The next easiest kind of vector addition problem is the kind in which the vectors to be added are
at right angles to each other. Let’s consider a relative velocity problem involving that kind of
vector addition problem.
Example 11-2
A boy sitting in a car that is traveling due north at 65 mph aims a BB gun (a gun
which uses a compressed gas to fire a small metal or plastic ball called a BB), with a
muzzle velocity of 185 mph, due east, and pulls the trigger. Recoil (the backward
movement of the gun resulting from the firing of the gun) is negligible. In what
compass direction does the BB go?
Defining
v to be the velocity of the car relative to the road,
CR
v to be the velocity of the BB relative to the car, and
BC
v to be the velocity of the BB relative to the road; we have
BR
NORTH
v = 185 mph
BC
EAST
v
= 65 mph
CR
v
BR
θ
vBC
tan θ = v
CR
v
1
−
BC
θ = tan v
CR
mph
185
θ tan 1−
=
mph
65
θ = 70.6°
The BB travels in the direction for which the compass heading is 70.6°.
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