Question

A water slide is constructed so that swimmers, starting from rest at the top of the slide, leave the end of the slide traveling horizontally. As the drawing shows, one person hits the water 5.00 m from the end of the slide in a time of 0.378 s after leaving the slide. Ignore friction and air resistance, find the height H in the drawing.

Answer 1

9.63 m

Step-by-step explanation:

We know that

Δx = vt.

Therefore, v = Δx / t

v = 5 / 0.378

v = 13.23 m/s

h = ½gt, so that

h = ½ * 9.8 * 0.378²

h = 4.9 * 0.1429

h = 0.7 m

Finally, using the law of conservation of energy, we know that

½mv² = mg(H - h)

½v² = g(H - h)

½v²/g = H - h, substituting the values and solving, we have

(½ * 13.23²) / 9.8 = H - 0.7

(½ * 175) / 9.8 = H - 0.7

87.5 / 9.8 = H - 0.7

8.93 = H - 0.7

H = 8.93 + 0.7

H = 9.63 m