[In this question, the unit vectors $$\(\mathbf{i}\)$$ and $$\(\mathbf{j}\)$$ are in a vertical plane, $$\(\mathbf{i}\)$$ being horizontal and $$\(\mathbf{j}\)$$ being vertically upwards.] A small ball is projected with velocity $$\((6 \mathbf{i}+12 \mathbf{j}) \mathrm{m} \mathrm{s}^{-1}\)$$ from a fixed point $$\(A\)$$ on horizontal ground. The ball hits the ground at the point $$\(B\)$$, as shown in Figure 5. The motion of the ball is modelled as a particle moving freely under gravity. (a) Find the distance $$\(A B\)$$. (4) When the height of the ball above the ground is more than $$\(h\)$$ metres, the speed of the ball is less than $$\(10 \mathrm{~ms}^{-1}\)$$ (b) Find the smallest possible value of $$\(h\)$$. (4) When the ball is at the point $$\(C\)$$ on its path, the direction of motion of the ball is perpendicular to the direction of motion of the ball at the instant before it hits the ground at $$\(B\)$$. (c) Find, in terms of $$\(\mathbf{i}\)$$ and $$\(\mathbf{j}\)$$, the velocity of the ball when it is at $$\(C\)$$. (3)

Answer:

Knowledge points:

Solution: