Question

Two friends Raman and Madhav arc playing on the bank of a river. They are throwing stones in the river. Raman is a student of the science stream whereas Madhav from the commerce stream. Every time Raman throws the stone far away than Madhav. Madhav was surprised and could not understand the reason. Finally, Raman explained the fact that it is relating to physics. (i) Which concept is being used here? (ii) What is the minimum angle to get the maximum horizontal range?​

Answer 1

Newton's third law and conservation of momentum

Explanation:

• The concept of science here is conservation of momentum according to which the stone thrown in water pushes the water downwards , and in reaction to that the stone is pushed upwards.
• Newton's third law also explains this phenomena where in the force exerted by the stone on the water is equal and opposite to that of the force exerted by the water on the stone.
• If no air resistance is considered , then the minimum possible angle for maximum possible range is 45 degrees. Explanation for the same is given below: Range is given by :

        $R = \frac{u^2sin2\theta}{g}$

       Therefore , $sin2\theta = 1$ ( maximum value possible)

                            $2\theta = 90$ deg

                            $\theta = 45$ deg

                    Hence 45 degrees is the minimum angle for which maximum range is possible.