A particle with total energy E is moving in a potential energy region U(x). Motion of the particle is restricted to the region when

Vectors $$\overrightarrow A ,\overrightarrow B $$ and $$\overrightarrow C $$ are such that $$\overrightarrow A .\overrightarrow B = 0$$ and $$\overrightarrow A .\overrightarrow C = 0$$. Then the vector parallel to $$\overrightarrow A $$ is

One coolie takes 1 minute to raise a suitcase through a height of 2 m but the second coolie takes 30 s to raise the same suitcase to the same height. The powers of two coolies are in the ratio

A person holding a rifle (mass of person and rifle together is 100 kg) stands on a smooth surface and fires 10 shots horizontally, in 5 s. Each bullet has a mass of 10 g with a muzzle velocity of 800 m s^$$-$$1. The final velocity acquired by the person and the average force exerted on the person are :