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Collision 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 twocar 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 twocar system after the collision:
.
Hint A.2 The component of the final velocity in the eastwest direction
Find the component of
in the eastwest direction.
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View Full DocumentHint A.2.1 Find the eastwest component of the initial momentum
What is
, the magnitude of the total momentum
of the two cars in the eastwest
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:
(eastwest) =
Correct
Hint A.3 Find the northsouth component of the final momentum
Find the component of
in the northsouth direction.
Hint A.3.1 Find the northsouth component of the initial momentum
What is the magnitude
of the total momentum
of the two cars in the northsouth
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:
(northsouth) =
Correct
Hint A.4 Math help
Let
be the eastwest component of
, and
the northsouth 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 eastwest component of
, and
the northsouth 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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 Spring '10
 PICKETT
 Physics, Mass

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