Question

A 1500 kg aircraft going 30 m/s collides with a 3000 kg aircraft that is parked and they stick together after the collision and are going 10 m/s after the collision. If they skid for 131.3 m before stopping, how long (in seconds) did they skid?

Answer 1

Given that this is an completely inelastic collision, So Using momentum conservation:

Pi = Pf

m1u1 + m2u2 = (m1 + m2)V

m1 = mass of aircraft 1 = 1500 kg

m2 = mass of aircraft 2 = 3000 kg

u1 = Initial speed of m1 = 30 m/sec

u2 = Initial speed of m2 = 0 m/sec

So,

V = (1500*30 + 3000*0)/(1500 + 3000) = 10 m/sec

So both aircrafts are going at 10 m/sec after collision

Now given that they skid 131.3 m before stopping, So

Using 3rd kinematic equation:

Vf^2 = Vi^2 + 2*a*d

d = skid distance = 131.3 m

Vi = Initial speed of both aircrafts after collision = 10 m/sec

Vf = final speed of both aircrafts after collision = 0 m/sec

So,

a = (Vf^2 - Vi^2)/(2*d)

a = (0^2 - 10^2)/(2*131.3) = -0.381 m/sec^2

Now Using 1st kinematic equation:

Vf = Vi + a*t

t = (Vf - Vi)/a

t = (0 - 10)/(-0.381)

t = 26.25 sec = time for which both aircrafts skid

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