Question #31858

A bird flies in the east direction with a speed of 5 ms−1. The wind is blowing towards north at a

speed of 3 ms−1. Determine the relative velocity of the bird with respect to the wind. Draw

appropriate diagram for solving the problem.

(b) A plane is flying with a constant speed along a straight line at an angle of 30° with the

horizontal. The weight of the plane is 80, 000 N and its engine provides a thrust of 100, 000 N in

the direction of flight. Two additional forces are exerted on the plane: the lift force perpendicular

to the plane’s wings, and the force due to air resistance opposite to the direction of motion. Draw

the free-body diagram showing all forces on the plane. Determine the lift force and the force due

to air resistance. (2 + 4)

2. A bus is moving downhill at a slope of 5° on a rainy day. At the moment when the speed of the

bus is 30 km h−1, the driver spots a deer 30 m ahead. He applies the brakes and comes to a stop.

The deer is paralyzed by fear and does not move. Will the bus stop before reaching it or will it hit

the deer? Do relevant calculations and draw appropriate force diagram. Take the coefficient of

kinetic friction to be μk = 0.26. (10)

3. Derive an expression relating impulse and linear momentum. In a safety test, a car of mass 1000

kg is driven into a brick wall. Its bumper behaves like a spring (k = 5 × 106 Nm−1) and is

compressed by a distance of 3 cm as the car comes to rest. Determine the initial speed of the car.

speed of 3 ms−1. Determine the relative velocity of the bird with respect to the wind. Draw

appropriate diagram for solving the problem.

(b) A plane is flying with a constant speed along a straight line at an angle of 30° with the

horizontal. The weight of the plane is 80, 000 N and its engine provides a thrust of 100, 000 N in

the direction of flight. Two additional forces are exerted on the plane: the lift force perpendicular

to the plane’s wings, and the force due to air resistance opposite to the direction of motion. Draw

the free-body diagram showing all forces on the plane. Determine the lift force and the force due

to air resistance. (2 + 4)

2. A bus is moving downhill at a slope of 5° on a rainy day. At the moment when the speed of the

bus is 30 km h−1, the driver spots a deer 30 m ahead. He applies the brakes and comes to a stop.

The deer is paralyzed by fear and does not move. Will the bus stop before reaching it or will it hit

the deer? Do relevant calculations and draw appropriate force diagram. Take the coefficient of

kinetic friction to be μk = 0.26. (10)

3. Derive an expression relating impulse and linear momentum. In a safety test, a car of mass 1000

kg is driven into a brick wall. Its bumper behaves like a spring (k = 5 × 106 Nm−1) and is

compressed by a distance of 3 cm as the car comes to rest. Determine the initial speed of the car.

Expert's answer

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