A rescue helicopter wants to drop a package of supplies to isolated mountain climbers on a rocky ridge 200 m below. If the helicopter is traveling horizontally with a speed of 70 m/s (250 km/h), (a) how far in advance of the recipients (horizontal distance) must the package be dropped? (b) Suppose, instead, that the helicopter releases the package a horizontal distance of 400 m in advance of the mountain climbers. What vertical velocity should the package be given (up or down) so that it arrives precisely at the climbers' position? (c) With what speed does the package land in the latter case?

Question

Physics

Krystal Meza

5 December, 11:53

A rescue helicopter wants to drop a package of supplies to isolated mountain climbers on a rocky ridge 200 m below. If the helicopter is traveling horizontally with a speed of 70 m/s (250 km/h), (a) how far in advance of the recipients (horizontal distance) must the package be dropped? (b) Suppose, instead, that the helicopter releases the package a horizontal distance of 400 m in advance of the mountain climbers. What vertical velocity should the package be given (up or down) so that it arrives precisely at the climbers' position? (c) With what speed does the package land in the latter case?

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Answers (1)

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Cohen Cross · Answer 1

a) 447.21m

b) - 62.99 m/s

c) 94.17 m/s

Explanation:

This situation we can divide in 2 parts:

⇒ Vertical : y = -200 m

y = 1/2 at²

-200 = 1/2 * (-9.81) * t²

t = 6.388766 s

⇒Horizontal: Vx = Δx/Δt

Δx = 70 * 6.388766 = 447.21 m

b) ⇒ Horizontal

Vx = Δx/Δt ⇒ 70 = 400 / Δt

Δt = 5.7142857 s

⇒ Vertical:

y = v0t + 1/2 at²

-200 = v (5.7142857) + 1/2 * (-9.81) * 5.7142857²

v0 = - 7 m/s ⇒ it's negative because it goes down.

v = v0 + at

v = - 7 + (-9.81) * 5.7142857

v = - 62.99 m/s

c) √ (70² + 62.99²) = 94.17 m/s