7. -1 points HRW10 2.P059 My Notes Ask Your Teacher Water drips from the nozzle

Question

7. -1 points HRW10 2.P059 My Notes Ask Your Teacher Water drips from the nozzle of a shower onto the floor 156 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. (a) Find the location of the third drop as measured from the nozzle of the shower when the first drop strikes the floor. cm below the nozzle (b) Find the location of the second drop as measured from the nozzle of the shower when the first drop strikes the floor. cm below the nozzle Additional Materials Section 2.5 Algebra-Squareroots & Squares

Explanation / Answer

Let the drops fall at time interval of t
Let the first drop fall at time 0.
Then 2nd drop falls at t
3rd drop at 2t
4th drop at 3t

Let height to which every drop falls = h
Time taken to fall = sqrt(2h/g)
Time interval between first drop and fourth drop = 3t
When first drop hits the floor, then 4th drop begins to fall.
Therefore, 3t = sqrt(2h/g)
Or, t = 1/3 * sqrt(2h/g) -----------(2)

2nd drop falls at t. Therefore, at time 3t, the second drop has spent time 3t - t = 2t.
Distance of 2nd drop from the nozzle = 1/2 * g * (2t)^2 = 1/2 * g * 4t^2
= 2gt^2
= 2g * 1/9 * 2h/g [using the value of t from (1)]
= 4/9 * h
= 4/9 * 156 cm = 69.33 cm

3rd drop falls at 2t. Therefore, at time 3t, the second drop has spent time 3t - 2t = t.
Distance of 3rd drop from the nozzle = 1/2 * g * (t)^2
= 1/2 * g * 1/9 * 2h/g [using the value of t from (1)]
= h/9 = 156/9 cm = 17.33 cm

Ans: 2nd drop is 69.33 cm below the nozzle and
3rd drop is 17.33 cm below the nozzle.

Related Questions

Navigate

• Browse (All)
• Browse 7
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.