Vectors in mechanics

A particle P of mass 0.4 k moving with velocity 7i ms¹ when it receives

Find the two possible values of λ

[In this question, i and j are horizontal perpendicular unit vectors.]

A particle A has mass 3 kg and a particle B has mass 2 kg.

The particles are moving on a smooth horizontal plane when they collide directly.

Immediately before the collision, the velocity of A is (3i – j) m s^–1 and the velocity of B is (–6i + 2j) m s^–1 Immediately after the collision the velocity of A is 2i m s

Find the total kinetic energy of the two particles before the collision.

Find, in terms of i and j, the impulse exerted on A by B in the collision.

Find, in terms of i and j, the velocity of B immediately after the collision.

A particle P of mass 2 kg is moving with velocity (4i 3j) m s¹when it receives an impulse (6i 42j) N s.

Find the speed of P immediately after receiving the impulse.

The angle through which the direction of motion of P has been deflected by the impulse is α °

Find the value of α

A particle P has mass 0.5 kg. It is moving in the xy plane with velocity 8im s⁻¹ when it receives an impulse λ (− i + j) N s, where λ is a positive constant.

The angle between the direction of motion of P immediately before receiving the impulse and the direction of motion of P immediately after receiving the impulse is θ°

Find (i) the value of λ

the value of θ

[In this question, i and j are perpendicular unit vectors in a horizontal plane.]

Figure 3 represents the plan view of part of a smooth horizontal floor, where AB is a fixed smooth vertical wall. The direction of AB is in the direction of the vector (i + j)

A small ball of mass 0.25 kg is moving on the floor when it strikes the wall AB. Immediately before its impact with the wall AB, the velocity of the ball is (8i + 2j)m s⁻¹

Immediately after its impact with the wall AB, the velocity of the ball is vm s⁻¹ The coefficient of restitution between the ball and the wall is

By modelling the ball as a particle,

show that v = 4i + 6j

Find the magnitude of the impulse received by the ball in the impact.

A particle P of mass 0.5 kg is moving with velocity (4i + 3j) m s^–1 when it receives an impulse J N s. Immediately after receiving the impulse, P is moving with velocity (–i + 6j) m s^–1.

Find the magnitude of J.

The angle between the direction of the impulse and the direction of motion of P immediately before receiving the impulse is α

Find the value of α

[In this question, i and j are perpendicular unit vectors in a horizontal plane.]

Figure 1 represents the plan view of part of a smooth horizontal floor, where AB represents a fixed smooth vertical wall.

A small ball of mass 0.5 kg is moving on the floor when it strikes the wall.

Immediately before the impact the velocity of the ball is (7i + 2j) m s^–1.

Immediately after the impact the velocity of the ball is (i + 6j) m s^–1.

The coefficient of restitution between the ball and the wall is e.

Show that AB is parallel to (2i + 3j).

Find the value of e.