What is the time that the water fell?????

Question

Water drips from the nozzle of a shower onto the floor 240 cm below. The drops fall at regular (equal) intervals of time, the first drop striking the floor at the instant the fourth drop begins to fall. Find the locations (above the floor in cm) of the second and third drops when the first strikes the floor. Second drop?

Third drop?

Answer 1

The time t for a drop to fall distance h is given by:

h = gt^2 / 2 where g is the acceleration due to gravity.

t^2 = 2h / g ...(1)

When the first drop strikes the floor, the second drop has been falling for time 2t / 3, and the third

drop for time t / 3, and the fourth drop for time 0.

The distance s2 fallen by the 2nd drop is:

s2 = g(2t / 3)^2 / 2

= 2gt^2 / 9

Substituting for t^2 from (1):

s2 = 4h / 9

The height above the floor of the 2nd drop is:

h - s2 = 5h / 9

= 5 * 240 / 9

= 133 cm. to 3sf.

The distance s3 fallen by the 3rd drop is:

s3 = g(t / 3)^2 / 2

= gt^2 / 18

Substituting for t^2 from (1):

s3 = h / 9

The height above the floor of the 3rd drop is:

h - s3

= 8h / 9

= 8 * 240 / 9

= 213 cm. to 3sf.