A rescue plane wants to drop supplies to isolated mountain climbers on a rocky r

Question

A rescue plane wants to drop supplies to isolated mountain climbers on a rocky ridge 235 m below. Assume the plane is traveling horizontally with a speed of 215 km/h (59.7 m/s).

Figure 3-37
(a) How far in advance of the recipients (horizontal distance) must the goods be dropped (Figure 3-37a)?
_____ m
(b) Suppose, instead, that the plane releases the supplies a horizontal distance of 425 m in advance of the mountain climbers. What vertical velocity (up or down) should the supplies be given so that they arrive precisely at the climbers' position (Figure 3-37b)? (Assume up is positive.)
______ m/s
(c) With what speed do the supplies land in the latter case?
________ m/s

Explanation / Answer

a) How far in advance of the recipients (horizontal distance)must the goods be dropped (Figure 3-37a)? since g - 9.8 m/s2 and t is a subject to height h. We willhave t=v(2h/g) The horizontal distance S is then S=Vh t and S= Vh v(2h/g) S= 59.7 v(2 x 235 /9.8) S= 413 m (b) Suppose, instead, that the plane releases the supplies ahorizontal distance of 425 m in advance of the mountain climbers.What vertical velocity (up or down) should the supplies be given sothat they arrive precisely at the climbers' position (Figure3-37b)? (Assume up is positive.) Since the supplies are released early ( we needmore time in the air) the initial vertical velocity must be upwardwhile horizontal velocity will remain the same. Total time t to travel distance S with horizontal velocity Vhis t= S/Vh where t=t1 + t2 +t3 t1=t2=t' (tine to go up and return back to the plane'slevel t3 - time to fall to the ground from planes level t1+ t2 = (S - S0)/Vh Where S=425 m S0= 413 m t'= (t1+ t2)/2 Then Vv= gt' Vv=g(S - S0)(2Vh) Vv = 9.8(425 - 413)/(2x59.7) Vv=0.985 m/s (c) With what speed do the supplies land in the lattercase? Once the object leaves the plane it will have the same horizontalcomponent Vh ( assumeing no air ressitance) while the verticalcomponent Vv will be same as in part (b) V = v(Vh2 + Vv2) V = v((59.7)^2 + (20.3)^2) V= 63 m/s

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