Momentum and impulse in vector formEdexcel International A Level Further Maths: Mind map

Exam questions on Momentum and impulse in vector form

1. A ball of mass $0.4$ kg is moving with velocity $(6\mathbf{i}+8\mathbf{j})$ m s$^{-1}$ when it is hit by a bat. Immediately after being hit it moves with velocity $(-2\mathbf{i}+5\mathbf{j})$ m s$^{-1}$. The unit vectors $\mathbf{i}$ and $\mathbf{j}$ are perpendicular and lie in a horizontal plane.
   Find the angle between the direction of the impulse and the vector $-\mathbf{i}$.2 marks
2. Two particles $A$ and $B$, of masses $2$ kg and $3$ kg, move on a smooth horizontal plane and collide. Before the collision $A$ has velocity $(4\mathbf{i}-\mathbf{j})$ m s$^{-1}$ and $B$ has velocity $(-2\mathbf{i}+3\mathbf{j})$ m s$^{-1}$. After the collision $A$ has velocity $(-\mathbf{i}+2\mathbf{j})$ m s$^{-1}$. The unit vectors $\mathbf{i}$ and $\mathbf{j}$ are perpendicular and lie in the plane.
   Find the speed of $B$ after the collision.2 marks
3. A tennis ball of mass $0.06$ kg is moving with velocity $(-20\mathbf{i}+5\mathbf{j})$ m s$^{-1}$ when it is struck by a racket. The racket exerts an impulse of $(3\mathbf{i}+1.5\mathbf{j})$ N s on the ball. The unit vectors $\mathbf{i}$ and $\mathbf{j}$ are perpendicular and lie in a horizontal plane. Ignore the weight of the ball.
   Find the velocity of the ball immediately after it is struck.3 marks