Motion in a Pla...

A projectile is thrown in the upward direction making an angle of 60° with the horizontal direction with velocity of 147 ms ^-1. Then, the time after which its inclination with the horizontal is 45°, is

Two bodies are projected from ground with equal speed 20 ms ^-1 from the same position in the same vertical plane to have equal range but at different angles above the horizontal. If one of the angle is 30° the sum of their maximum heights is (assume, g =10 ms ^-2)

Three particles A, B and C are projected from the same point with the same initial speeds making angles 30°, 45° and 60°, respectively with the horizontally. Which of the following statements is correct?

A point P moves in counter-clockwise direction on a circular path as shown in the figure. The movement of P is such that it sweeps out a length s = t³ + 5, where s is in metre and t is in second. The radius of the path is 20 m. The acceleration of P, when t = 2 s is nearly

A car is circulating on the path of radius r and at any time its velocity is v and rate of increase of velocity is a. The resultant acceleration of the car will be

If kinetic energy of the particle of mass m performing UCM in a circle of radius r is E. Find the acceleration of the particle

A bob of mass M is suspended by a massless string of length L. The horizontal velocity v at position A is just sufficient to make it reach the point B. The angle θ at which the speed of the bob is half of that at A, satisfies

A roller coaster is designed such that riders experience `weightlessness' as they go round the top of a hill whose radius of curvature is 20 m. The speed of the car at the top of the hill is between

A particle of mass m is tied to one end of a string of length l and rotated though the other end along a horizontal circular path with speed v. The work done in half horizontal circle is

A cyclist is travelling on a circualr section of highway of radius 2500 ft at the speed of 60 mile h ^-1. The cyclist suddenly applies the brakes causing the bicycle to shown down at constant rate. Knowing that after 8s, the speed has been reduced to 45 mile h ^-1. The acceleration of the bicycle immediately after the brakes have been applied is