A small object of mass 0.2 kg rests at a point O on a rough horizontal surface. The coefficient of friction between the object and the surface is 0.5. A force of magnitude P N acting at an angle θ below the horizontal is applied to the object. The velocity of the object is v m s¯¹ away from O at time t s after the force begins to act (see diagram). It is given that tan θ = ¾ and that P = 0.4t for 0 ≤ t ≤ 8.

A cylindrical container is open at the top. The curved surface and the circular base of the container are both made f...

A particle P is projected with speed 20 m s¯¹ at an angle of 60° below the horizontal, from a point O which is 30 m a...

The diagram shows a uniform lamina ABCD with AB = 0.75 m, AD = 0.6m and BC = 0.9 m. Angle BAD = angle ABC = 90°. [Fig...

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 ...