Consider a drop of rain water having mass 1 g falling from a height of 1 km. It hits the ground with a speed of 50 m s^$$-$$1. Take 'g' constant with a value 10 m s^$$-$$2. The work done by the (i) gravitational force and the (ii) resistive force of air is

A particle moves from a point $$\left( { - 2\widehat i + 5\widehat j} \right)$$ to $$\left( {4\widehat j + 3\widehat k} \right)$$ when a force of $$\left( {4\widehat i + 3\widehat j} \right)$$ N is applied. How much work has been done by the force ?

What is the minimum velocity with which a body of mass m must enter a vertical loop of radius R so that it can complete the loop?

A body of mass 1 kg begins to move under the action of a time dependent force $$\overrightarrow F = \left( {2t\widehat i + 3{t^2}\widehat J} \right)N,$$ where $${\widehat i}$$ and $${\widehat j}$$ are unit vectors along x and y axis. What power will be developed by the force at the time t ?