Perfectly Inelastic momentum question

[Jm4872]

Homework Statement

Two ice-fishermen are driving trucks across a frozen and frictionless lake. Truck 1 (m1 = 920kg) is traveling with a speed of 16.3m/s in a direction of 57.4degrees SOUTH of EAST. Truck 2 (m2 = 930kg) is traveling due NORTH with a speed of 24.9m/s. The trucks collide and lock into a single unit. What is the speed of the joined trucks immediately after the collision?

Homework Equations

p=mv

The Attempt at a Solution

because this is a perfectly inelastic collision and I'm looking for the final velocity of the objects i used the following equation:
m₁v₁+m₂v₂=(m₁+m₂)v_f


the values i inputed were :
(920*16.3)+(930*24.9)=(930+920)v_f

I then solved for v_f and got the answer 20.6 m/s however this answer is not right and I'm not sure what is wrong?
The program is giving me the hint; This is a perfectly inelastic collision. The total momentum of the system (2 trucks) is the same before and after the collision. After the collision, the total mass moves with a single velocity. Don't forget that momentum is a vector and that speed is a scalar.
But its not really helping me, I understand that speed is supposed to be scalar which is why I'm using 16.3 m/s instead of breaking it into its components

 

[weesiang_loke]

hi,
when using the equation of conservation of momentum, we need to consider the direction of the velocity. and that's what the hint trying to tell you.
so in this case we need to resolve the velocity both trucks into two components, like x-component and y-component.
then we have for x-component:
m₁v_1x + m₂v_2x = (m₁+m₂)v_fx;
so v_1x = v₁ cos (57.4) (consider eastwards as positive direction);
and v_2x = 0
thus 920*16.3*cos57.4=(930+920)v_fx

similarly for the y-component (along north-south axis).

i think this should solve your problem.