A balloon starts rising from ground,vertically upwards,uniformly at rate of 1m/s.At end of 4sec a body was released from balloon.Calculate the time taken by released body to reach ground?

The height of balloon after 4s is 1/2 * 4×4 =8m. The speed after 4s is 0+4*×1=4m/s. When the body is separated from the body it carries is inertia by the virtue of which is velocity is same at that moment=4m/s but it`s acceleration changes to -g instantly. That means it will move upwards with initial bel=4m/s and acceleration = -10m/s. The time of accent of body is 4/10s = 0.4s. height risen= 4×0.4 +1/2× -10×0.4×0.4 =0.8 m. Therefore the total height attained by body is 8+0.8 m= 8.8m. now it is at rest under acceleration of gravity. By second equation of motion time of descent comes to be t= √{(2×8.8)/10}=√1.76s . Total time taken after release is 0.4+√1.76=0.4+1.33=1.73s.