1. A 10 kg bowling ball is rolling down the lane at 5 m/s when it collides with
ID: 249590 • Letter: 1
Question
1. A 10 kg bowling ball is rolling down the lane at 5 m/s when it collides with a stationary pin. The pin flies straight at 8 m/s, and the bowling ball continues rolling forward at 2 m/s. What was the mass, in kg, of the pin? *
2. A car of mass 1000 kg at rest at a stop light is hit from behind when a second car of mass 900 kg moving at a speed of 13.4 m/s, collides with it. If the two cars lock bumpers, what common speed do they move off with after the collision?
3. An astronaut of mass 30-kg stands motionless space holding a bag of ten baseballs. The baseballs have a mass of 0.145 kg each and the total mass of the balls and bag is 1.70-kg. The astronaut takes one baseball out of the bag and throws it with a velocity of 7.00 m/s due west. What is the velocity of the astronaut after she throws the baseball? (Give your answer in cm/s)
Explanation / Answer
(1) Applying conservation of momentum:
10*5 = m*8 + 10*2
=> m*8 = 30
=> m = 30/8 = 3.75 Kg
Hence the mass of the pin is 3.75 Kg.
(2) Let the common speed of both the cars is v.
Now,
1000 * 0 + 900 * 13.4 = (1000+900) * v
=> v = 900*13.4/1900 = 6.35 m/s
(3) Initially, astronaut and balls are standstill.
Now, applying conservation of momentum:
[(30 + (1.70-0.145)]*v + 0.145*7 = 0
=> [31.555]*v = -0.145*7
=> v = -0.0322 m/s = -3.22 cm/s
The negative sign in above shows that the direction of the velocity of astronaut shall be in the opposite direction that of the ball i.e., in the east direction.
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