A ball of mass 100 gm is projected vertically upwards from the ground with a velocity of 49 m/sec. At the same time another identical ball is dropped from a height of 98 m to fall freely along the same path as that followed by the first ball. After some time the two balls collide and stick together and finally fall to the ground. Find the time of flight of the masses.

Answer

`6.53 s`

Explanation

`((1)/(2) g t^(2)) + (49t - (1)/(2) t^(2)) = 98`
`rArr t = 2s u_(1) = g t(hat(j)) = -19.6hat(j)m//s`
`u_(2) = (u - g t)hat(j) = +29.4hat(j) m//s`
`v_(1) (u_(1) + u_(2))/(2) = 4.9 m//s`
`h = 4.9 xx 2 (1)/(2) xx 9.8 xx 2 xx 2 = 78.4m`
For the combined mass
`x = ut + (1)/(2) xx 9.8 t^(2), t = 4.53`
`:.` Total time of height
`= 2 + 4.53 = 6.53 sec`.