A railway engine of mass 120000kg is towing a coach of mass 60000kg up a straight track inclined at an angle of α to the horizontal where sin α = 0.02. There is a light rigid coupling, parallel to the track, connecting the engine and coach. The driving force produced by the engine is 125000N and there are constant resistances to motion of 22000 N on the engine and 13000N on the coach.

A particle P moves in a straight line starting from a point O and comes to rest 35 s later. At time t s after leaving...

Two particles of masses 1.2 kg and 0.8 kg are connected by a light inextensible string that passes over a fixed smoot...

A small ball is projected with speed 15 m s¯¹ at an angle of 60° above the horizontal. Find the distance from the poi...

The variables x and y satisfy the equation yⁿ = Ax³, where n and A are constants. It is given that y = 2.58 when x = ...

The parametric equations of a curve are x = 2t + sin 2t, y = 1 – 2 cos 2t, for −½π < t < ½π.

The variables x and θ satisfy the differential equation x cos² θ (dx/dθ) = 2 tan θ + 1, for 0 ≤ θ < ½π and x > 0. It ...