A railway carriage of mass 11 tonnes started moving down a plane from rest. The plane was inclined to the horizontal at an angle whose sine is , and the resistance to the carriage’s motion was 16 kg-wt per tonne of the carriage’s mass. The carriage reached the bottom of the plane after covering a distance of 144 m, and then it collided with another carriage of the same mass that was at rest. Given that the two carriages coupled together as a result of the impact then came to rest 50 seconds later, determine the distance covered by the two carriages on the horizontal road. Consider the acceleration due to gravity to be .
Two smooth spheres of masses 83 g and 37 g were moving in a straight line. At time seconds, where , the spheres’ displacements relative to a fixed point are given by and , respectively, where is a fixed unit vector. Given that the two spheres collided and coalesced into one body, determine the speed of this composite body and the magnitude of the impulse between the spheres.
A ball of mass 125 g moving at a constant speed of 50 m/s passed a certain point and, 3 minutes later, another ball of mass 75 g passed the same point. It was moving at 80 cm/s and accelerating at 4 cm/s2. The two balls collided and coalesced into one ball. Determine the time taken for the second ball to hit the first and the speed of the coalesced body after the impact.