inelastic collision problem AP Physics?

Question

a 1500 kg car traveling east at 25 m/s and a 3000kg minivan traveling south at 16.7 m/s collide at a perpendicular intersection. Assuming that the collision is completetely inelastic, what is the velocity of the vehicles immediately after collsion? (answer is 13.9 m/s at 53.1 degress south of east) how do you do this?

i have this already
(1500kg)(25 m/s) + (3000kg)(16.7m/s)= Vab(4500kg)
Vab= 19.5 m/s
what's next?

Answer 1

m1*v1 + m2*v2 = (m1+m2)*v3

lets start by calculating in the x direction of V. The car is traveling purely in the x direction while the van's velocity has no x component (it is traveling south).

1500*25 + 3000*0 = (1500+3000)Vx
37500 = 4500 Vx
Vx = 8.333

in the y direction:

1500*0 + 3000*(-16.7) = (1500 + 3000)Vy
50100 = 4500Vy
Vy = -11.1333

So the resultant vector is traveling south east. Now using Pythagorean theorem calculate the magnitude:

sqrt(-11.1333^2 + 8.333^2) = 13.9 m/sec

and to get the angle:

arctan(8.3333/11.13333) = south 36.8 deg east

Answer 2

I got the answer for the velocity but not the direction. Well you have to remember to conserve momentum in both the x and y axis. The east will be x axis and the south will be the y axis.
In the x axis we have only one mass and one velocity. so the equation would be (3000kg)(16.7m/s)=(4500kg)(v). the velocity is only in the x axis. solving that equation we get the velocity in the x axis to be 11.13 m/s.
Now we must find the velocity in the y axis. Again we only have one object moving in the y axis which is the car. The equation would be (1500kg)(25 m/s)=(4500kg)(v). Solving that equation we get a velocity of 8.33 m/s in the y axis.
Now that we have a velocity in each of the axis we can use the pythagorean theorem to find the final velocity.
we set one side of the triangle equal to 11.13 m/s and the other to 8.33 m/s. Now you just find the answer for the hypotenuse and that will be the velocity of the two objects together.
Hope this Helps.

Answer 3

well you have the right idea concerning the conservation of momentum. however, in order to add them directly you have to assume that the cars are moving in the same direction.

However, since momentum is a vector quantity, the direction makes an impact on the outcome. In order to get the right answer you have to take the two cars momentums and directions.

Since one car is going south and the other is going north, it makes our calculations easier. the angle between the cars is 90 degrees, thus we can use the pythagorean theorm.

--------1500kg---------->
| \
| \
| \
| \ Resultant
| \
V V
3000 kg

I know its a crude drawing but I hope you get the point.
the momentum for the first car is 1500(25)= 37500
the momentum for the second car is 3000(16.7)=50100
using the pythagorean theorm we get the resultant momentum as (37500^2+ 50100^2)^(1/2)= 62580
using the final mass as 4500(due to inelastic) the final velocity comes to be v=momentum/mass= 62580/4500= 13.9m/s

The angle is also used with the triangle. a=angle

tan(a)=opp/adj tan(a)=50100/37500 tan(a)=1.336 a=arctan(1.336 ) a=53.1 degress south of east.

Answer 4

I think you need to consider the x direction and the y direction seperately, like vector quantities.

First, try to get the x velocity after the collision.
Then the y velocity after the collision.
Draw these vectors in a triangle and solve for the diagonal. Then also use the triangle and a little trig to get the direction.

Answer 5

It is harder without a diagram (-: