Two identical balls are shot upwards one after another . . .

Question : Two identical balls are shot upwards one after another at an interval of 2s, along the same vertical line with same initial velocity of 40 m/s. The balls collide n seconds after the first ball is shot. What is the value of n?

Doubt by Suhani

Solution :

Initial velocity (u) = 40 m/s
acceleration (a) = -g

The two balls will collide after n seconds after the first ball is shot.

Using II equation of motion

s=ut+½at²

Displacement covered by first ball in n seconds = Displacement covered by second ball in (n-2) seconds

sn=s(n-2)

40(n)+½(-g)(n)² = 40(n-2)+½(-g)(n-2)²
40n-½gn²=40n-80-½g(n²+4-4n)

-½gn²=-80-½gn²-2g+2ng
0=-80+2ng-2g

80=+2g(n-1)

80=2(9.8)(n-1)
80/2 = 9.8(n-1)

40/9.8 = n-1

4.08+1=n

n=5.08

n=5 (approx)

Hence, the required value of n is 5.