PHYS 2211 Module 9.5

Collisions in Multiple Dimensions

Recommended Reading

9.5 Collisions in Multiple Dimensions

Learning Objectives

By the end of this section, you will be able to:

  • Express momentum as a two-dimensional vector
  • Write equations for momentum conservation in component form
  • Calculate momentum in two dimensions, as a vector quantity


Practice 9.5.1
An 80-g particle moving with an initial speed of 50 m/s in the positive x direction strikes and sticks to a 60-g particle moving 50 m/s in the positive y direction. How much kinetic energy is lost in this collision?
(a) 96 J
(b) 89 J
(c) 175 J
(d) 86 J
(e) 110 J
Practice 9.5.2
A 5.0-g particle moving 60 m/s collides with a 2.0-g particle initially at rest. After the collision each of the particles has a velocity that is directed 30° from the original direction of motion of the 5.0-g particle. What is the speed of the 2.0-g particle after the collision?
(a) 72 m/s
(b) 87 m/s
(c) 79 m/s
(d) 94 m/s
(e) 67 m/s
Practice 9.5.3
A 4.2-kg object, initially at rest, “explodes” into three objects of equal mass. Two of these are determined to have velocities of equal magnitudes (5.0 m/s) with directions that differ by 90°. How much kinetic energy was released in the explosion?
(a) 70 J
(b) 53 J
(c) 60 J
(d) 64 J
(e) 35 J


Consider how you would answer these questions. Then bring this to class for a group discussion.

Because of your interest in the environment and your physics experience, you have been asked by the Campus Museum of Natural History to assist in the production of an animated film about hawks. In the script, a 1.5-kg hawk hovers motionless with respect to the ground when it sees a goose flying below it. The hawk dives straight down. It strikes the goose at a speed of 60 km/hr and digs its claws into the goose’s body. The 2.5 kg goose was flying north at 30 km/hr just before it was struck by the hawk and killed instantly. The animators want to know the velocity of the hawk and dead goose just after the strike.