4 A constant resistance to motion of magnitude 350 N acts on a car of mass 1250 kg . The engine of the car exerts a constant driving force of 1200 N . The car travels along a road inclined at an angle of \(\theta\) to the horizontal, where \(\sin \theta = 0.05\). Find the speed of the car when it has moved 100 m from rest in each of the following cases.
- The car is moving up the hill.
- The car is moving down the hill.
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Two particles \(A\) and \(B\), of masses 0.4 kg and 0.2 kg respectively, are connected by a light inextensible string which passes over a fixed smooth pulley. Both \(A\) and \(B\) are 0.5 m above the ground. The particles hang vertically (see diagram). The particles are released from rest. In the subsequent motion \(B\) does not reach the pulley and \(A\) remains at rest after reaching the ground.
- For the motion before \(A\) reaches the ground, show that the magnitude of the acceleration of each particle is \(\frac { 10 } { 3 } \mathrm {~m} \mathrm {~s} ^ { - 2 }\) and find the tension in the string.
- Find the maximum height of \(B\) above the ground.