A400-kg stopped at an intersection is rear-ended by a 1600-kg truck moving at 10 m/s. if the car was in neutral and the brakes were off, so that the collision is approximately elastic, find final velocity of the car if the truck was moving 5 m/s after the collision.

The sum of the momenta before and after the collision will be the same.  Before the car's momentum was 0 and the truck's was P=mv, P=1600*10=16000kgm/s
Afterward the truck has momentum P=1600*5=8000kgm/s
So the car gets the rest of what we started with Pcar=(16000-8000)=8000kgm/s
So the car's velocity was Pcar=mv,  Pcar/m = v,   8000/400=20m/s

The velocity the wave was traveling at before the transmitter converts it to a sound wave is 3.0 x 10⁸ m/s.

Velocity of waves

The velocity of waves is the rate of change of the wave's displacement with time.

The velocity of waves is determined by taking the product of the wave's frequency and wavelength.

v = fλ

v = 13,000 x 23,076

v = 3.0 x 10⁸ m/s.

Thus, the velocity the wave was traveling at before the transmitter converts it to a sound wave is 3.0 x 10⁸ m/s.

Learn more about velocity of waves here:  link