Question

At an intersection, a 1500 kg car traveling east at 25 m/s collides with a 2500 kg van traveling north at 20 m/s. Find the direction and magnitude of the velocity of the wreckage immediately after the collision, assuming that the vehicles undergo a perfectly inelastic collision (that is, they stick together)

Answer 1

Step-by-step explanation:

Mass of the car, m = 1500 kg

Initial speed of the car, u = 25 m/s east

Mass of the van, m' = 2500 kg

Initial speed of van, u' = 20 m/s north

It is assumed that the vehicles undergo a perfectly inelastic collision. The law of conservation of linear momentum gives the velocity after the collision as :

`mu+m'u'=(m+m')V\\\\V=(mu+m'u')/((m+m'))\\\\V=(1500* 25i+2500* 20j)/((1500+2500))\\\\V=(37500i+50000j)/(4000)\\\\V=(37500i)/(4000)+(50000j)/(4000)\\\\V=(9.37i+12.5j)\ m/s`

Magnitude of velocity,

`|V|=√(9.37^2+12.5^2) =15.62\ m/s`

Direction,

`\tan\theta=(12.5)/(9.37)=53.14^(\circ)`