A large disc has its center hinged to the ground about which it rotates with a constant angular speed. A small car fitted with a gun is fixed at the periphery of the disc (fig 27.1, 27.2). Points A and B are marked in the figure for reference.
The gun always faces the central axis of rotation and the size of the gun is set such that, when inclined, it prevents anything from getting into the car. The gun harmonically changes its angles of inclination with horizontal (rising out of the horizontal plane) with upper and lower bounds of π/2 and 0 radians respectively. It opens up every time near A with a period equal to that of the rotation of the disc. Mass of the car and gun is negligible relative to the disc, mass of the bullet is 1 Kg and that of the disc is 20 Kg.
When the car crosses B for the third time, a bullet is fired.
1. For the bullet to land back into the car in 2 seconds:
(a) The magnitude of air resistance force if air always blows from north to south is _
(b) The velocity with which it should be fired is _*
2. If the bullet manages to land back into the car in 2 seconds:
(a) The distance it covers on y axis is _
(b) The kinetic energy of the disc when the bullet is at its maximum height is _
*Rational answer (till 2 decimal places)
Rest of the answers must be integers. Neglect friction.
[Use: 3π = 9.4, π² = 10, g = 10 ms⁻²]
