In a court hearing, a physicist reconstructs an accident in the following way. A
ID: 2259761 • Letter: I
Question
In a court hearing, a physicist reconstructs an accident in the following
way. A sports car of mass m1=1000kg collided with a parked truck of
mass m2=1500kg. From the skid marks, it is estimated that the speed of
the truck immediately after the collision was 21.6m/s, at an angle of
33.7 degrees with respect to the direction of the incoming sports car. The sports
car left skid marks at an angle of 60 degrees to its initial direction, but did not
stop, leaving the scene of the accident badly damaged.
(a) Determine the speed of the sports car immediately after the collision.
(b) Determine the initial speed of the sports car in units of m/s and
miles/hour. The accident occurred on a quiet residential street. Was the
sports car speeding?
Explanation / Answer
Let sports car be coming from left to right (say along x-axis)
Let truck go upwards at the given angle.
So
momentum along x is conserved
So
1000*u=1500*21.6cos(33.7)+1000*vcos(60)
So
2u=53.91+v
momentum along y is conserved
So
0=1500*21.6sin(33.7)-1000*vsin(60)
So
v=20.758m/s=46.434miles/hour (speed of sports car afterwards)
u=37.33m/s=83.505 miles/hour (initial speed of sports car)