# Velocity after a collision

## Homework Statement

A car with a mass of 1200 kg and a speed of 70 km/h collides in a head-on collision with a motorcycle. The vehicles lock together and continue along with the speed of 45 km / h in the cars original direction. The motorcycle weighing 250 kg.
What is the speed of the motorcycle before the collision?
(The masses of both the are included in the weights given)

## The Attempt at a Solution

Okay, I'm having a hard time with this one.

I've tried to do something like this:

m= 1200kg

v= 70km/h = 19.4m/s

1200*19.4 = 23280N = 23.3kN

1200*19.4+250*x (why I tried something like this is because I had seen a similar problem being solved along these lines, but on that problem all the information was given, so I thought I could solve this by simply giving the motorcykle the speed of X. However I do not understand this at all, so I thought I'd come here and ask for help to put me into the right direction. I'd like to understand every answer I write and you guys are always to a great help.

## Answers and Replies

tiny-tim
Science Advisor
Homework Helper
Hi Fishingaxe! … I thought I could solve this by simply giving the motorcykle the speed of X.

Yes, you're right, you can!

If you carry on, you should get an equation which you can solve for X. can someone confirm if the answer is 12.88m/s.

I think I am waaaaaaaaaaaay off.

For a similar problem the calculation looked like this: (6,0kg)(5,0m/s)+(2,0kg)(-8m/s)/8=1,75m/s

So I did: (1200kg)(19.4m/s)+(250kg)(x)/19.4(maybe it's /x?) then I got 23280+250x/19.4 which is hard to solve? I must be a retard on some level. This is probably obvious for most of you.. :s Maybe I am doing a wrong equation?

P=mv
ptot=p1+p2
ptot=(m1+m2)*v

p1=23280
p2=250*x
ptot=(1200+250)*12.5

18125 = 23280 - 250x
250x = 5155
x=20.62

Answer: the velocity of the motorcycle is 20.62 m/s.

Is this correct?

tiny-tim
Science Advisor
Homework Helper
Hi Fishingaxe! (just got up :zzz:)

I'm not really understanding your equation. It should be total-momentum-before = total-momentum-after.​

EDIT: ooh, you just replied again, hold on I'll have a look! tiny-tim
Science Advisor
Homework Helper
ptot=(m1+m2)*v

p1=23280
p2=250*x
ptot=(1200+250)*12.5

Yes, that's the correct method! However, the answer is not in the correct units …

the question gave all the speeds in km/hr, so shouldn't the answer should be in km/hr also? There was no need to convert!

Yes, that's the correct method! However, the answer is not in the correct units …

the question gave all the speeds in km/hr, so shouldn't the answer should be in km/hr also? There was no need to convert!

Okay, so the answer should be written as 74.2km/h? :)

tiny-tim
Science Advisor
Homework Helper
i don't get 74.2 i don't get 74.2 Hm, if the v for the motorcycle is 20.62m/s then the v for it in km/h should be 20.62*60*60?

tiny-tim
Science Advisor
Homework Helper
can you do it in km/hr throughout (ie without converting to m/s and back)?

Hm, if the v for the motorcycle is 20.62m/s then the v for it in km/h should be 20.62*60*60?
Nope.

p=mv

p1 = 1200*70 = 84000

p2 = 250*x

ptot (1200+250)*45

65250 = 84000-250x

250x = 18750

x=75

So the velocity is 75km/h.

I am a bit confused though. If I got when I measured in m/s, 20.62m/s. Why shouldn't the speed be, 20.62*60(seconds in 1 minute)*60(minutes in one hour). Then the answer becomes 74232m/h = 74.2km/h?

And what is the correct method to convert m/s to km/h?

Nope.

1 meter / second = 3.6 km/h so what was wrong?

tiny-tim
Science Advisor
Homework Helper
65250 = 84000-250x

250x = 18750

x=75

So the velocity is 75km/h.

yup! (and can you see how much simpler that is?)
I am a bit confused though. If I got when I measured in m/s, 20.62m/s. Why shouldn't the speed be, 20.62*60(seconds in 1 minute)*60(minutes in one hour). Then the answer becomes 74232m/h = 74.2km/h?

you must have made a mistake somewhere And what is the correct method to convert m/s to km/h?

3.6 ?

yup! (and can you see how much simpler that is?)

you must have made a mistake somewhere 3.6 ?

Ah, I used too few decimals when I converted 70km/h to m/s. I used 19.4 instead of 19.44444 ;)A

Thanks for your help :D