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A block \(D\) of weight 50 N lies at rest in equilibrium on a fixed rough horizontal surface. A force of magnitude 15 N is applied to \(D\) at an angle \(\theta\) to the horizontal (see diagram).
- Complete the diagram in the Printed Answer Booklet showing all the forces acting on \(D\).
It is given that \(D\) remains at rest and the coefficient of friction between \(D\) and the surface is 0.2 .
- Show that
$$15 \cos \theta - 3 \sin \theta \leqslant 10 .$$
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A golfer hits a ball from a point \(A\) with a speed of \(25 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle of \(15 ^ { \circ }\) above the horizontal. While the ball is in the air, it is modelled as a particle moving under the influence of gravity. Take the acceleration due to gravity to be \(10 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).
The ball first lands at a point \(B\) which is 4 m below the level of \(A\) (see diagram). - Determine the time taken for the ball to travel from \(A\) to \(B\).
- Determine the horizontal distance of \(B\) from \(A\).
- Determine the direction of motion of the ball 1.5 seconds after the golfer hits the ball.
The horizontal distance from \(A\) to \(B\) is found to be greater than the answer to part (b).
- State one factor that could account for this difference.