Question

A 2100 kg truck is traveling east through an intersection at 2.0 m/s when it is hit simultaneously from the side and the rear. (Some people have all the luck!) One car is a 1200 kg compact traveling north at 5.0 m/s. The other is a 1500 kg midsize traveling east at 10 m/s. The three vehicles become entangled and slide as one body. What is their velocity (magnitude and direction) just after the collision?

Answer 1

speed is
`3.41` meter per second and direction is
`66.25` degrees

Step-by-step explanation:

As per the conservation of momentum theory, Initial momentum is equal to final momentum

`Pi_(1200) + Pi_(1500) + Pi_(2100) = Pf_(1200) + Pf_(1500) + Pf_(2100) \\m_(1200) * v_(1200) + m_(1500) * v_(1500) + m_(2100) * v_(2100) = [ m_(1200) + m_(1500) + m_(2100)] * V_f`

Substituting the given values we get

Velocity in horizontal direction

`1200 * 5 + 0 + 2100 * 2 = 4800 * V_(fx)\\V_(fx) = 1.375 (m)/(s)`

Velocity in vertical direction

`1500*10 = 4800 * V_(fx)\\V_(fx) = 3.125 (m)/(s)`

Final velocity

`√(1.375 ^2 + 3.125^2)\\3.41=`

Direction of the velocity

`\alpha = tan^(-1) (3.125)/(1.375) \\= 66.25`

So speed is
`3.41` meter per second and direction is
`66.25` degrees