This

**preview**has**blurred**sections. Sign up to view the full version! View Full DocumentCollision at an Angle
Two cars, both of mass
, collide and stick together. Prior to the collision, one car had been
traveling north at speed
, while the second was traveling at speed
at an angle
south of
east (as indicated in the figure). After the collision, the two-car system travels at speed
at
an angle
east of north.
Part A
Find the speed
of the joined cars after the collision.
Hint A.1 Determine the conserved quantities
Which of the following statements is true for the collision described?
ANSWER:
Momentum is conserved but kinetic energy is not conserved.
Kinetic energy is conserved but momentum is not conserved.
Both kinetic energy and momentum are conserved.
Neither kinetic energy nor momentum is conserved.
Correct
Apply conservation of momentum:
.
Find both components (north and east) of the initial momentum
using the information
in the problem introduction. The magnitude of
is equal to the magnitude of the
momentum vector for the two-car system after the collision:
.
Hint A.2 The component of the final velocity in the east-west direction
Find the component of
in the east-west direction.

Hint A.2.1 Find the east-west component of the initial momentum
What is
, the magnitude of the total momentum
of the two cars in the east-west
direction? (Take eastward to be positive, westward negative.)
Express your answer in terms of
,
, and
.
ANSWER:
=
Correct
Now use the conservation of momentum equation to find
.
Express your answer in terms of
and
.
ANSWER:
(east-west) =
Correct
Hint A.3 Find the north-south component of the final momentum
Find the component of
in the north-south direction.
Hint A.3.1 Find the north-south component of the initial momentum
What is the magnitude
of the total momentum
of the two cars in the north-south
direction? (Take northward to be positive, southward negative).
Express your answer in terms of
,
, and
.
ANSWER:
=
Correct
Express your answer in terms of
and
.
ANSWER:
(north-south) =
Correct
Hint A.4 Math help
Let
be the east-west component of
, and
the north-south component. Then
.
You will also need to use the following trignometric identity when you evaluate the right-
hand side of the above equation in terms of
and
:
.
Express your answer in terms of
and
.

ANSWER:
=
Correct
Part B
What is the angle
with respect to north made by the velocity vector of the two cars after the
collision?
Hint B.1
A formula for
Let
be the east-west component of
, and
the north-south component. Then
,
since the angle asked for is the angle east of north.
Express your answer in terms of
. Your answer should contain an inverse trigonometric
function.
ANSWER:
=
Correct
A Ball Hits a Wall Elastically
A ball of mass
moving with velocity
strikes a vertical wall.
The angle between the ball's initial velocity

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