# physics mechanic

2.

(a) A rescue plane wants to drop supplies to isolated mountain climbers on a rocky range ridge 200m below. If the plane is travelling horizontally with a speed of 80ms-1, how far in advance of the recipients must the goods be dropped?

(b) Suppose, instead, that the plane releases the supplies a horizontal distance of 400m in advance of the mountain climbers. What vertical velocity should they give the supplies so that they arrive precisely at the climbers&#039; position? With what speed do the supplies land in this case? Comment on the results.

( Ans: (a) 506m (b) -15ms-1, 113.6ms-1 )

Rating

(a) In vertical motion part, its time of flight can be found as:

s = ut + at2/2

with s = 200, u = 0 and a = 10

t = 6.32 s

So, in horizontal direction, it has flied for 6.32 x 80 = 506 m

(b) Now the time of flight is 400/80 = 5 s

So in vertical direction, it should fall a distance of 200 m in 5 s:

s = ut + at2/2

with s = 200, t = 5 and a = 10

200 = 5u + 125

u = 15 m/s

Also, it vertical velocity of landing is:

v2 - u2 = 2as with u= 15, a = 10 and s = 200

v = 65 m/s

In addition to its horizontal velocity of 80 m/s, by Pyth thm, the resultant velocity is 113.6 m/s

Source(s): Myself