1) Find the final velocity of the two balls if the ball with velocity

Question

v2i = −21.0 cm/s has a mass equal to half that of the ball with initial velocity
v1i = +26.7 cm/s. (Indicate the direction with the sign of your answer.)
*just confused on how to solve for V1f / V2f=42cm/s*

2) A 2.62 kg object initially moving in the positive x-direction with a velocity of +5.43 m/s collides with and sticks to a 1.98 kg object initially moving in the negative y-direction with a velocity of -3.03 m/s. Find the final components of velocity of the composite object. (Indicate the direction with the sign of your answer.) ( vfx = m/s vfy = m/s)

3) A 1,275-kg car traveling initially with a speed of 25.0 m/s in an easterly direction crashes into the rear end of a 9,400-kg truck moving in the same direction at 20.0 m/s The velocity of the car right after the collision is 18.0 m/s to the east. (I solved for part a, which states what is the velocity of the truck right after the collision? which equals (20.9495m/s east), confused on how to answer part(b). The figure numbers shows before +25.0m/s plus +20.0m/s which yields after that is +18.0m/s plus part a answer (20.9495m/s east)

(b) How much mechanical energy is lost in the collision?

please any help would be wonderful

Answer 1

first off, since V1f / V2f are both speeds, their ratio cannot be in m/s
It will just be a number.

All of these problems are the same, and involve conservation of momentum. In each case, you need

m₁v₁ + m₁v₁ = m₂v₂ + m₂v₂

By the time you plug in the given numbers, you can solve for the unknown value. Be sure to be careful with the signs on the velocities.