Linear momentum collision problem calculations 2

Questions 

1.     A toy truck with a mass of 3 kg was moving at 3 ms^-1 and hit with another toy truck of 1 kg and was moving with a velocity of 1 ms^-1, in the opposite direction. After collision, both trucks moved together in the same direction, calculate the common velocity of the two objects after collision.

 

m₁u₁ + m₂u_{2 =  (}m₁+ m₂₎v

            (3)(3) + (1)(-1) = (3+1)v

            9 – 1 = 4v

            v = 2 ms^-1

 

2.     A hunter shot a 100g bullet from a 1.5kg gun. If the bullet travelled 200 ms-1 after being triggered, what is the backward jerk of the gun. (Think final backward velocity of the gun).

 

Total initial momentum = Total final momentum = 0

m₁u₁ + m₂u_{2 =} 0

1.5(v) + 0.1(200) = 0 ß make sure to convert 100g to kg

1.5v +20 = 0

v = - 13.3 ms-1   ß Value is negative because gun moved in opposite direction

 

3.     A trolley of mass 2 kg was in a stationary condition, before a 5 g sticky plasticine was thrown into it with a velocity of 500 ms-1. After hitting the trolley, the plasticine sticks into it. Calculate the final velocity of both the trolley and plasticine?

Use the classic formula of momentum conservation

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

0.005 (500) + 2 (0) = (0.005+ 2)v

2.5 = 2.005v

 v = 1.245 ms^-1