The total mass of a cyclist and her bicycle is 75 kg. The cyclist ascends a straight hill of length 0.7 km inclined at 1.5° to the horizontal. Her speed at the bottom of the hill is 10 m s⁻¹ and at the top it is 5 m s⁻¹. There is a resistance to motion, and the work done against this resistance as the cyclist ascends the hill is 2000 J. The cyclist exerts a constant force of magnitude F N in the direction of motion. Find F.

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...

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 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)).