Question

4 balls are dropped from the top of a tower at intervals of one-one second. the first ball reaches the ground after 4s of dropping. what are the distances between first and second, second and third, third and fourth balls at this instant

Answer 1

When the ball is dropped, let say the height from where it drops is h.

So according to the formula of time of flight (for first ball which reaches the ground in 4secs) is:

Time = √(2h/g) (g is acceleration due to gravity=9.8m/s^2)

On putting the values and solving it the height comes out to be, h =78.4m.

So this means all four balls are dropped from height 78.4m with a gap of 1sec each, and all will reach the ground in 4sec(this is because all the balls are dropped as the first one, also they are dropped from same height).

Now using equation motion,

s = u*t + 0.5*g*t*t —(1) (s = it +(1/2)gt^2,. Both of these are same equations).

So as the ball is dropped, therfore initial velocity = 0.

When the first ball toch the ground, time is 4sec, so for the second ball time for which it has travelled is 3sec(because first and second ball are thrown with a gap of 1sec)

Using equation (1),

s1 = 0*3 + 0.5*9.8*3*3 (for second ball distance we have to find which it has travelled, time is 3sec, value of g=9.8m/s^2)

s1=44.1m

So as first ball touches the ground, distance travelled by it is 78.4 and at that instant second ball travels 44.1 m

Hence at that instant distance between first and second ball is (78.4–44.1) = 34.3m.

Now at that same instant third ball has travelled for 2sec, because the balls are dropped with a gap of 1sec each.

Using the same equation(equation (1)) for third ball,

s2 = 0*2 + 0.5*9.8*2*2

s2=19.6m

Hence at that same instant distance between second and third ball is (44.1–19.6) = 24.5m

Now at that instant fourth ball has travelled for 1sec, because balls are dropped with a gap of 1sec each.

Hence using the same equation (equation (1)) for the fourth ball,

s3 = 0*1 +0.5*9.8*1*1

s3 = 4.9m

Therefore at that same instant distance between third and fourth ball is (19.6–4.9) = 14.7m