2D Momentum question ..?

Question

I can’t figure this out. Please help me if you can:

A car of mass 750 kg travelling North collided with a truck of mass 2000 kg, which was travelling East. The truck was travelling at 10m/s, and after the collision the car and the truck stuck together and moved in a direction of North 53 o East. Was the car initially exceeding 16.67 m/s ??

Thanks!

Answer 1

straight forward question of equality as  (m1 x v1)^2 + (m2 x v2)^2 = ((m1+m2) v3) ^2

but since you have 2 different directions (east & west), you have to use the Pythagorean theorem to break them into what the missing value was. you know the mass of the vehicles and the momentum of one and what would the momentum of the other be. have fun.

Answer 2

Let the velocity of the car be v  m/s. Its momentum -= 750*v. N

The momentum of the truck is  2000*10= 20000 E

   750*v / 20000 = tan (53) = 1.33

   ∴  v = 1.33 * 20000/750 = 35.47 m/s

yes the car was exceeding 16.67 m/s