Linear Motion

1. Determine the horizontal velocity u with which a stone must be projected from point p of height h so that it may hit the inclined plane perpendicularly. Inclination is theta and inclined plane is kept just below point p at ground. Give the value in terms of g, h and cot theta.                                                                                                                                                                                                                                                                                             2. Point A moves uniformly with velocity v so that vector v is continually aimed at point B which in its turn moves rectilinearly with velocity u<v. Initially, u perpendicular to v and separation was l. How soon will the points converge.     Plz answer both the questions as I have exam tommorow.

An engine is hauling a train of mass M kg a level track at a constant speed v m/s. The resistance due to friction is f N/kg. What extra power must the engine develop to maintain the speed up a gradient of h in s:

A car starts from rest with an acceleration of 6 m/s2 which decreases to zero linearly with time, in 10 seconds, after which the car continues at a constant speed. Find the time required for the car to travel 400 m from the start.

The upper half of an inclined plane with an inclination a, is perfectly smooth, while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom, if the coefficient of friction for the lower half is given by:

a 2m wide truck is moving with a uniform speed of 8m/s along a straight horizontal road. a pedestrian starts crossing the road at an instant when the truck is 4m away from him. the minimum constant velocity with which he should run so as to avoid the accident