A car of mass 800 kg is moving up a hill inclined at θ° to the horizontal, where sin θ = 0.15. The initial speed of the car is 8 m s⁻¹. Twelve seconds later the car has travelled 120 m up the hill and has speed 14 m s⁻¹.

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 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 ...

Let f(x) = (5x² + x + 27) / ((2x + 1)(x² + 9)).