Hi I needed some help solving this sum on coefficient of friction. I tried solving it but the quantities cancel out on both sides.?

A light plane of mass 1200 kg makes an emergency landing on a short runway. With its engine off, it lands on the runway at a speed of 35 m/s. A hook on the plane snags a cable attached to a 130 kg sandbag and drags the sandbag along. Now you can consider the system as a combined mass along with the sandbag and the plane.

Now, the coefficient of friction between the sandbag and the runway is µk = 0.4, and also the plane’s brakes give an additional retarding force of magnitude 1400 N. So our target for this problem is to find how far does the plane go before it comes to stop.

Assume, when the plane snags the sandbag, the collision is instantaneous. [Hint: Think carefully whether you can apply conservation of momentum or not]

(a) Find the speed of the plane and sandbag immediately after the collision.

(b) Find the time when the plane along with the sandbag will come to stop. [Hints: Think about whether the system (sandbag and the plane) will accelerate or decelerate.]

 (c) Find how far the plane goes before it comes to stop.

Physics14 hours ago