Enjoy carefully chosen collisions word problems along with their solutions.

**Word problem #1:**

A marble with a weight of 3 grams moving at 2 m/s collides with another marble at rest weighting also 3 grams.

a. Calculate the speed of the two stuck-together marbles **immediately** after colliding.

b. Calculate the speed again if the weight of the marble at rest is 6 grams.

**Solution:**

First, convert 3 grams to kilograms since the unit of momentum is kg.m/s

1 kilogram = 1000 grams, so 3 grams = 0.003 kg

a. net momentum (before) = net momentum (after)

net mv (before) = net mv (after)

0.003 kg × 2 m/s + 0.003 kg × 0 m/s = (0.003 kg + 0.003 kg) × speed (after)

0.006 kg.m/s + 0 = 0.006 kg × speed (after)

0.006 kg.m/s = 0.006 kg × speed (after)

0.006 kg.m/s
0.006 kg

= speed (after)
speed (after) = 1 m/s

This result was not difficult to predict. Since after colliding the mass is twice what it was before, the speed has to be half what it was before collision.

b. We solve this question the same way except this time we use a mass of 6 kg.

0.003 kg × 2 m/s + 0.003 kg × 0 m/s = (0.003 kg + 0.006 kg) × speed (after)

0.006 kg.m/s + 0 = 0.009 kg × speed (after)

0.006 kg.m/s = 0.009 kg × speed (after)

0.006 kg.m/s
0.009 kg

= speed (after)
speed (after) = 0.6666 m/s.

**Word problem # 2:**

A billiard ball (Ball #1) going with a speed of 3 m/s hits another billiard ball (ball #2) at rest. What is the speed of the ball #2 as it moves away?

**Solution:**

The trick here is to see that since both ball are billiard balls, we don't need to actually know what the masses are equal to to solve the problem. Second, notice that after ball #1 hits ball #2, it comes to rest, so the speed is 0.

mass × 3 m/s + mass × 0 m/s = mass × 0 + mass × v (after)

mass × 3 m/s = mass × v (after)

mass × 3 m/s
mass

= speed (after)
speed (after) = 3 m/s

**Word problem # 3:**

A 2000-kg car going 30 m/s collides head-on with a 5000-kg truck going at the same speed. If the truck comes to a halt, what happens to the car? (Suppose the vehicles hit each other at the bumpers)

**Solution: **

Suppose going to the right is positive.

Suppose also that the car is going to the right, then the truck is going to the left. The speed of the car is positive while that of the truck is negative.

2000 kg × 30 m/s + 5000 kg × -30 m/s = 5000 kg × 0 m/s + 2000 kg × speed

60000 kg.m/s + -150000 kg.m/s = 5000 kg × 0 m/s + 2000 kg × speed

-90000 kg.m/s = 2000 kg × speed

-90000 kg.m/s
2000 kg

= speed (after)
speed = -45 m/s

The car will move backward with a speed of 45 m/s.

Hopefully the collisions word problems solved above made sense to you. Thanks for reading!