In a harbour, wind is blowing at the speed of 72 km/h and the flag on the mast of a boat anchored in the harbour flutters along the N-E direction. If the boat starts moving at a speed of 51 km/h to the north, what is the direction of the flag on the mast of the boat?

A cyclist is riding with a speed of 27 km/h. As he approaches a circular turn on the road of radius 80 m, he applies brakes and reduces his speed at the constant rate of 0.50 m/s every second. What is the magnitude and direction of the' net acceleration of the cyclist on the circular turn?

Two towns A and B are connected by a regular bus service with a bus leaving in either direction every T minutes. A man cycling with a speed of 20 km h~1 in the direction A to B notices that a bus goes past him every 18 min in the direction of his motion, and every 6 min in the opposite direction. What is the period T of the bus service and with what speed - (assumed constant) do the buses ply on the road?

A trolley of mass 200 kg moves with a uniform speed of 36 km/ h on a frictionless track. A child of mass 20 kg runs on the trolley from one end to the other (10 m away) with a speed of 4 m s^-1 relative to the trolley in a direction opposite to the its motion, and jumps out of the trolley. What is the final speed of the trolley? How much has the trolley moved from the time the child begins to run?

A trolley of mass 300 kg carrying a sandbag of 25 kg is moving uniformly with a speed of 27 km/h on a frictionless track. After a while, sand starts leaking out of a hole on the floor of the trolley at the rate of 0.05 kg s^-1 . What is the speed of the trolley after the entire sand bag is empty?

A police van moving on a highway with a speed of 30 km h_ 1 fires a bullet at a thief’s car speeding away in the same direction with a speed of 192 km h^-1 . If the muzzle speed of the bullet is 150 m s^1 with what speed does the bullet hit the thief’s car ? (Note: Obtain that speed which is relevant for damaging the thief’s car).

The speed of a boat is 5 km/h in still-water. It crosses a river of width 1 km along the shortest path in 20 min. The velocity of river water in km/h is

A car moving along a straight highway with a speed of 126 km h^-1 is brought to a stop within a distance of 200 m. What is the retardation of the car (assumed uniform), and how long does it take for the car to stop?

Onna two-lane road, car A is travelling with a speed of 36 km h_1. Two care B and C approach car A in opposite directions with a speed of 54'km h_1 each. vAt a certain instant, when the distance AB is equal to AC, both being 1 km,* B’ decides to overtake A before C does. What minimum acceleration of car B is required to avoid an accident?

Two trains A and B of length 400 m each are moving on two parallel tracks with a uniform speed of 72 km h^-1 in the same direction, with A ahead of B. The driver of B decides to overtake A and accelerates by 1 m//s^-2 . If after 50 s, the guard of B just brushes past the driver of A, what was the original distance between them?

Give the magnitude and direction of the net force acting onfa) a drop of rain falling down with a constant speed. (b) a cork of mass 10 g floating on water. (c) a kite skillfully held stationary in the sky. (cf) a car moving with a constant velocity of 30 km/h on a rough road.