# relative motion

• Apr 23rd 2007, 04:52 PM
roxig66
relative motion
Im trying to help my daughter and we are lacking information like a formula for relative velocity.. here is one of 20 problems and I am wishing someone could explain it enough that we can learn and do the rest. Thanks :)

Two cars are traveling inthe same direction. Car A is traveling 62mph. Car B is traveling 70mph. When car B passes car A, how fast does car b appear to be going to the passengers in car A? How much slower does car A appear to be going to the passengers of car B?
• Apr 23rd 2007, 05:13 PM
topsquark
Quote:

Originally Posted by roxig66
Im trying to help my daughter and we are lacking information like a formula for relative velocity.. here is one of 20 problems and I am wishing someone could explain it enough that we can learn and do the rest. Thanks :)

Two cars are traveling inthe same direction. Car A is traveling 62mph. Car B is traveling 70mph. When car B passes car A, how fast does car b appear to be going to the passengers in car A? How much slower does car A appear to be going to the passengers of car B?

The best way to look at these is to try to visualize the problem. Car B is moving in the same direction, so we automatically know that car B should be moving slower in the frame of car A than it is in the stationary (groud based) frame. Let that be your guide:
v = 70 mph - 62 mph = 8 mph

If you really want the formulae then I have to introduce some variables for you. Let us have two people: Stacy and Moe, and one moving object. We're going to put Stacy in the "stationary" frame, that is the one that isn't moving relative to the ground. We're going to assume Moe ("moving" frame) is moving at a constant velocity v (according to Stacy) relative to Stacy in the stationary frame.

Let the object be moving at a velocity vS according to Stacy and moving at velocity vM according to Moe.

Then
vS = vM + v

Note that these are all velocities and hence vector quantities, so this is a vector addition.

To apply this to your car problem, car B is your object, car A is Moe. Calling the direction of car A relative to the ground to be positive we have:
v = 62 mph (the velocity of car A relative to the ground)
vS = 70 mph (the velocity of car B relative to the ground)
vM = ? (the velocity of car B relative to car A)

vS = vM + v
70 mph = vM + 62 mph
vM = 70 mph - 62 mph = 8 mph
as I stated earlier.

-Dan
• Apr 24th 2007, 06:35 AM
roxig66
thank you
Thank you for the reply last night it helped my daughter understand relative motion problems more clearly. She was able to go and complete all of her application problems unassisted.

Roxanne
• Apr 24th 2007, 06:54 AM
topsquark
Quote:

Originally Posted by roxig66
Thank you for the reply last night it helped my daughter understand relative motion problems more clearly. She was able to go and complete all of her application problems unassisted.

Roxanne

Pleased to be of service! :)

-Dan