An Alaskan rescue plane drops a package of emergency rations to a stranded party of explorers. The plane is traveling horizontally at 40 m/sec at a height of 100 meters above ground.

Question

          a) Where does the package strike the ground relative to the point at which it was released?

           b) What is the vertical velocity component of the package when it hits the ground?

           c) What is the horizontal velocity component of the package when it hits the ground?

           d) With what velocity does it hit the ground?

Answer 1

(a)

First get the time in the air from

h = gt²/2 ⇒

t = √(2h/g)

Plug in

h = 100 m

g = 9.8 m/s²

and get t in seconds. Then multiply t by the constant horizontal speed.

x = vt

Plug in

v = 40 m/s

t = ? (result from above)

and get x in meters.

(b)

Vertical speed:

v(t) = v₀ + gt

Plug in

v₀ = 0

g and t from above

and get v(t) in m/s.

(c) It is the same as the initial velocity when released, which is 40 m/s.

(d) The horizontal component is the same as the answer for part (c). The vertical component is the result for part (b), in the downward direction.