Two boys conducted experiments on the projectile motion with stopwatch and noted some readings. As one boy throws a stone in air at the same angle with the horizontal, the other boy observes that after 4 ~s , the stone is moving at an angle 30^ to the horizontal and after another 2 ~s it is travelling horizontally. The magnitude of the initial velocity of the stone is (Acceleration due to gravity, g=10 ~ms ⁻² .)

Step-by-step solution

Given, acceleration due to gravity, g=10 ~m / s ^2 After 4 ~s , angle between stone and horizontal plane, =30^ After t=4 ~s , equation of the vertical projectile motion, when =30^ Total time to reach the stone at horizontal surface, t=2+4=6 ~s After t=6 ~s , equation of horizontal projectile motion, =0^ , 0^ = v -g(6) v 0 [ array c 0^ =1 0^ =0 array ] or v -g(6)=0 From Eq. (ii), At t=4 ~s , when particles travelling in horizontal direction, Now, magnitude of initial velocity, aligned & v= (v )^2+(V )^2 & [From Eqs.