Collisions Worksheet Honors:
Name:_____________________ Date:______
1. A 1,160-kg car traveling initially with a speed of 25.0 m/s in an easterly direction crashes into the rear end of a
9,900-kg truck moving in the same direction at 20.0 m/s (see figure below). The velocity of the car right after the
collision is 18.0 m/s to the east.
(a) What is the velocity of the truck right after the collision?(20.8 m/s east)
(b) How much mechanical energy is lost in the collision? (Use input values with an adequate number of significant
figures to calculate this answer.)(8.85 kJ)
2. Three carts of masses 4.0 kg, 10 kg, and 3.0 kg move on a frictionless track with speeds of v1 = 5.0 m/s,
v2 = 3.0 m/s, and v3 = -3.6 m/s. The carts stick together after colliding. Find the final velocity of the three
carts.(2.31 m/s)
3. A 5.00 g object moving to the right at +20.0 cm/s makes an elastic head-on collision with a 10.0 g object that is
initially at rest.
(a) Find the velocity of each object after the collision. (-6.67 m/s, 13.3 m/s)
(b) Find the percentage of the initial kinetic energy transferred to the 10.0 g object.(88.9 %)
4. A 10.0 g object moving to the right at 25.0 cm/s makes an elastic head-on collision with a 15.0 g object moving in
the opposite direction at 33.0 cm/s. Find the velocity of each object after the collision. (-44.6 cm/s, 13.4 cm/s)
5. A cart with mass 0.340 kg moving on a frictionless linear air track at 1.2 m/s strikes a second cart of unknown
mass at rest. The collision between the two carts is elastic. After the collision, the first cart continues in its original
direction at 0.66 m/s. a) What is the mass of the second cart? b) What is the velocity of the second cart after
impact? ( 0.0987 kg, 1.86 m/s)
6. Two billiard balls move toward one another. The balls have identical masses and assume that the collision is
elastic. If the initial velocities of the balls are +30 cm/s and -20 cm/s, what is the velocity of each ball after the
collision? ( -20 cm/s and +30 cm/s)
7. Find the final velocity of the two balls if the ball with the initial velocity -20 cm/s has a mass equal to half the ball
with the initial velocity of +30 cm/s. [ANSWER: 𝑣1 ′ = −3.0 𝑐𝑚𝑠 ; 𝑣2 ′ = +47 𝑐𝑚/𝑠]
8. A5.00 g object moving to the right at 20.0 cm/s makes an elastic head-on collision with a 10.0 g object that is
initially at rest. Find (a) the velocity of each object after the collision and (b) the fraction of the initial KE transferred
to the 10.0 g object. [(a) 𝑣1 ′ = −6.67 𝑐𝑚𝑠 𝑎𝑛𝑑 𝑣2 ′ =13.3 cm/s (b) 0.88]
(9) A 10.0 g object moving to the right at 20.0 cm /s makes an elastic head-on collision with a 15.0 g object moving
in the opposite direction at 30.0 cm/s. Find the velocity of each object after the collision. [𝑣1 ′ = −40.0 𝑐𝑚; 𝑣2 ′ =
10.0𝑐𝑚/𝑠]
(10) A 25.0 g object moving to the right at 20.0 cm/s overtakes and collides elastically with a 10.0 g object moving
in the same direction at 15.0 cm/s. Find the velocity of each object after the collision. [𝑣1 ′ = 17.1 𝑐𝑚; 𝑣2 ′ =
22.1𝑐𝑚/𝑠]
(11) A billiard ball rolling across a table at 1.50 m/s makes a head-on elastic collision with an identical ball. Find the
speed of each ball after the collision:
a. When the second ball is at rest. [𝑣1 ′ = 0.0 𝑚; 𝑣2 ′ = 1.50𝑚/𝑠]
b. When the second ball is moving toward the first at a speed of 1.00 m/s. [𝑣1 ′ = −1.00 𝑚; 𝑣2 ′ = 1.50 𝑚/𝑠]
c. When the second ball is moving away from the first at a speed of 1.00 m/s. [𝑣1 ′ = 1.00 𝑚; 𝑣2 ′ = 1.50 𝑚/𝑠]
(12) Two blocks of masses m1 = 2.00 kg and m2 = 4.00 kg are released from rest at a height of 5.00 m
on a frictionless track as shown below. The blocks undergo an elastic head-on collision. (a)
Determine the velocity of each block just before the collision (b) Determine the velocity of the
blocks immediately after the collision. (c) Determine the maximum height to which the masses will
rise after the collision.
m1= 2.00 kg
5m
m2 =4.00 kg
5m
ANSWERS: (a) 9.90 m/s for both (b) [𝑣1f=−16.5𝑚𝑠; 𝑣2f=3.30 𝑚/𝑠] (c) [h1f = 13.9 m and h2f = 0.56 m]
(13) A 7.0 g bullet is fired into a 1.5 kg ballistic pendulum. The bullet emerges from the block with a
speed of 200 m/s, and the block rises to a maximum height of 12 cm. Find the initial speed of the
bullet. [v=528 m/s]
(14) An 8.00 g bullet is fired into a 250 g block that is initially at rest on the edge of a table of 1.00 m
height. The bullet remains in the block and after the collision the block lands 2.00 m from the table’s
base. Determine the initial speed of the bullet. [ v = 142.9 m/s (about 320 mph)]
(15) A 12.0 g bullet is fired horizontally into a 100 g wooden block that is initially at rest on a
frictionless horizontal surface and connected to a spring of k = 150 N/m. If the bullet-block system
compresses the spring by a maximum of 80.0 cm, what was the velocity of the bullet at impact with
the block? [273 m/s].
(16) Two carts of equal mass, m = 0.250 kg, are placed on a frictionless track that has a light spring
of force constant k = 50.0 N/m attached to one end of it. The first car is given an initial velocity of
3.00 m/s to the right and the second cart is initially at rest. If the cars collide elastically, find (a) the
velocity of the cars just after the first collision [0.0 m/s and 3.0 m/s] (b) the maximum compression
in the spring [ x = 0.21 m]
3.00m/s
v=0
k=50.0 N/m
3.00m/s
v=0
k=50.0 N/m