Projectiles and vectors??!?

Question

A rescue plane wants to drop supplies to isolated mountain climbers on a rocky ridge 235m below. it is traveling horizontally at 250 km/h (69.4 m/s). Suppose that the plane releases the supplies a horizontal distance of 425m in advance of the mountain climbers.

Instead of dropping it, what vertical velocity (up or down) should tthe supplies be given so that they arrive precisely at the climbers position? (8.37 m/s down) == how do to get this?

With what speed do the supplies land in the latter case? (97.4 m/s) == how do u calculate this?

i know the answers i just need to know how to get them?

Answer 1

<< Instead of dropping it, what vertical velocity (up or down) should tthe supplies be given so that they arrive precisely at the climbers position? (8.37 m/s down) >>

The analysis of this problem is like so --- the time for the supplies to move horizontally for 425 meters is the same time it will take the supplies to reach the ground which is vertically 235 meters below.

The first formula to use is

X = Vx(T)

where

X = horizontal distance the supplies have to travel = 425 m (given)

Vx = horizontal component of the velocity = 69.4 m (given)

T = time for supplies to reach the target

Substituting appropriate values,

425 = 69.4(T)

and solving for "T",

T = 425/69.4

T = 6.12 sec.

To determine the initial vertical component of the velocity, use the formula

S = Vo(T)  + (1/2)gT^2

where

S = vertical distance of target = 235 m

Vo = initial velocity

T = 6.12 sec (as calculated above)

g = acceleration due to gravity = 9.8 m/sec^2 (constant)

Substituting appropriate values,

235 = Vo(6.12) + (1/2)(9.8)(6.12)^2

Solving for Vo,

Vo = 235 - (1/2)(9.8)(6.12)^2

Vo = 8.41 m/sec (actually, close enough with your 8.37 m/sec answer)

<< With what speed do the supplies land in the latter case? (97.4 m/s)>>

Use the formula,

Vf - Vo = gT

where

Vf = velocity which supplies will land

and all the other terms have been previously defined.

Substituting values,

Vf - 8.41= (9.8)(6.12)

and solving for Vf,

Vf = 68.4 m/sec

NOTE -- please check how/whyyou got an answer of 97.4 m/sec.