Question

A 1400 kg aircraft going 40 m/s collides with a 1500 kg aircraft that is parked and they stick together after the collision and are going 19.3 m/s after the collision. If they skid for 8.2 seconds before stopping, how far did they skid?

Answer 1

Explanation:

It is given that,

Mass of the aircraft 1, m₁ = 1400 kg

Mass of aircraft 2, m₂ = 1500 kg

Initially, the aircraft 2 is at rest, u₂ = 0

Initial speed of the aircraft 1, u₁ = 40 m/s

After the collision, the total speed of the system, V = 19.3 m/s

Time, t = 8.2 s

Since, two objects stick together it is a case of inelastic collision. The acceleration of the system is given by :

$a=\dfrac{V}{t}$

$a=\dfrac{19.3\ m/s}{8.2\ s}$

$a=2.35\ m/s^2$

Distance covered by the system before stopping is given by :

$x=\dfrac{1}{2}\times a\times t^2$

$x=\dfrac{1}{2}\times 2.35\times (8.2)^2$

x = 79.007 meters

Hence, this is the required solution.