11 A particle \(P\) of mass 1 kg is fixed to one end of a light inextensible string of length 0.5 m . The other end of the string is attached to a fixed point O , which is 1.75 m above a horizontal plane. P is held with the string horizontal and taut. P is then projected vertically downwards with a speed of \(3.2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
- Find the tangential acceleration of P when OP makes an angle of \(20 ^ { \circ }\) with the horizontal.
The string breaks when the tension in it is 32 N . At this point the angle between OP and the horizontal is \(\theta\).
- Show that \(\theta = 23.1 ^ { \circ }\), correct to \(\mathbf { 1 }\) decimal place.
Particle P subsequently hits the plane at a point A .
- Determine the speed of P when it arrives at A .
- Show that A is almost vertically below O .