Question

A 1000 kg aircraft going 25 m/s collides with a 1500 kg aircraft that is parked. They stick together after the collision and are going 10 m/s after the collision. If they skid for 12.7seconds before stopping, how far did they skid? Hint: Are the aircraft moving at a constant velocity after the collision or do they experience an acceleration?

Answer 1

Energy is conserved before and after the crash
Before collision
m1=1000kg & v1=25m/s,m2=1500kg & v2=0
After collision-
m=2500 v=10m/s
Just before the crash,total Energy=Kinectic energy=(1/2)*m1*(v1)^2+(1/2)*m2*(v2)^2
=(1/2)*1000*25J =12500J
Now,it comes to rest from 10m/s in 12.7s
?v=u+a*t 0=10+a*12.7 a=-0.7874m/s^2

Force due to friction=m*a=2500*0.7874=1968.5N
therefore total energy in skidding=F*d=1968.5*d
Energy is conserved through the process,
Therefore therefore total energy in skidding=12500J
12500=1968.5*d d=6.35m