Problem

5.

[In this question $\mathbf{i}$ and $\mathbf{j}$ are horizontal perpendicular unit vectors and position vectors are given relative to a fixed origin.]

In a game, a ball $B$ is rolled across a horizontal surface towards a fixed target. The ball is modelled as a particle moving with constant velocity.

At time $t=1\,\mathrm{s}$, the position vector of $B$ is $(-2\mathbf{i}+5\mathbf{j})\,\mathrm{m}$. At time $t=9\,\mathrm{s}$, the position vector of $B$ is $(10\mathbf{i}-3\mathbf{j})\,\mathrm{m}$.

(a) Find the velocity of the ball.

The position vector of the target is $(13\mathbf{i}-5\mathbf{j})\,\mathrm{m}$.

(b) Use the model to find the distance of $B$ from the target at time $t=7\,\mathrm{s}$.