Three cars are approaching an
Three cars are approaching an intersection. Car #1 has mass 1500kg and is driving East at 10 m/s. Car #2 has mass 2500 kg and isdriving North at 20 m/s. Car #3 has mass 2000 kg and is drivingSouth at 30 m/s.
a) If the three cars collide simultaneously and stick together,what is their final velocity (magnitude and direction)?
b) What fraction of the initial kinetic energy is lost in thecollision?
c) If the collision last 0.5 seconds, what is the magnitude ofthe average force exerted on car #1? You may neglect any effects offriction between the cars’ tires and the road during thecollision.
d) If the coefficient of kinetic friction between the cars’tires and the road is uk=0.3, how far do the cars skid after thecollision, before coming to rest?
please show the steps on how to solve each step.
Answer:
a] Use conservation of momentum for both horizontal and verticaldirections.
for horizontal direction:
1500(10) + 0 + 0 = (1500 + 2500 + 2000)Vx
=> Vx = 0.250 m/s
in vertical direction
0 + 2500(20) – 2000(30) = (6000)Vx
Vy = 1.667 m/s
so, the magnitude of the final velocity is:
and direction counter-clockwise from positive x axis (from east)is:
.
b] Fraction of energy lost =
Where 
and 
substitute the values to get the answer as a fraction.
c] Magnitude of average force on the car = change in momentum ofcar 1 / time
=> F = 1500(10 – 0.25)/0.5 = 29250 N.
d] The acceleration (deceleration) due to friction is:
a = – ukg = – 0.3(9.8) = – 2.94 m/s2.
now use 
Vf = 0
so, S = 0.483 m.
This is how far the cars travel after the collision.
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