A ball of mass 100 g is projected upwards from the ground with a velocity of 49m/s . At the same time another ball is dropped from a height of 98 m to fall freely along the same path as ball. After some time they collide and stick together and fall together. Find the time of flight

FIrst task is we find at waht time t and place x from the bottom they collide
for ball 1, g = 9.8

and for ball 2

solving the two equations we get
t = 2seconds
x = 78.4m

Now as they stick it’s an inelastic collision which can be solved by momentum conservation but we need their velocities first
ball 1 : v1 = 49 – 9.8*2 = 29.4
ball 2 v2 = -19.6

by momentum conservation
mv1 + mv2 = 2mv
v = (v1+v2)/2
v = 4.9m/s (upwards direction)

Now time to reach ground from this point onwards is


solving we get t = 4.83seconds
so total time of flight is
2 + 4.83 = 6.83 seconds