A challenge!

2007-01-01 12:34 am
A 150kg crate is released from an airplane travelling due east at an altitude of 8500m with a ground speed of 120m/s. The wind applies a constant force on the crate of 250N directed horizontally in the opposite direction to the plane's flight path. Where and when (with respect to the release location and time) does the crate hit the ground?

回答 (2)

2007-01-01 2:11 am
✔ 最佳答案
Something wrong in the answer provided by zip852hk for the part of finding the location.

For the time:
The only force acting on the crate is the gravitational pull. (Air resistance is neglected here) So,
s = ut + 1/2 at²
8500 = (0)t + 1/2 (g) t²【When released, the crate is VERTICALLY at rest】
t² = 17000/g
t = √(17000/g)
◆If you take g = 10 ms-2,
 t = √(17000/10) = 41.2 sec (3 sig. fig.)
◆If you take g = 9.8 ms-2,
 t = √(17000/9.8) = 41.6 sec (3 sig. fig.)

For the landing place:
The only force acting on the crate is the wind (250N). (Air resistance is also neglected here)
BUT NOTE THAT since the plane is travelling at 120 ms-1 when the crate is released, the crate has an initial horizontal speed of 120 ms-1 towards east.
From Newton's Second Law,
F = ma
250 = 150 a
a = 5/3 ms-2

s = ut + 1/2 at²
s = (120) √(17000/g) + 1/2 (-5/3) √(17000/g)²
【Since the wind is blowing WEST, the acceleration is opposite in direction with motion, a negative sign is added. t is the value taken from the above part】
s = (120) √(17000/g) - 42500/(3g)
◆If you take g = 10 ms-2,
 s = (120) √(17000/10) - 42500/(3 x 10) = 3530 m (3 sig. fig.)【East of release location】
◆If you take g = 9.8 ms-2,
 s = (120) √(17000/9.8) - 42500/(3 x 9.8) = 3550 m (3 sig. fig.)【East of release location】


Hope it helps! ^^
Wish you a Happy 2007!
參考: Myself
2007-01-01 12:50 am
very easy
first, consider vertically
s=ut+1/2at^2(u=0)
8500=1/2x10xt^2
t=41.2s
so u know when

and now what is the position?
consider the horizontal force
F=ma
250=150a
a=1.67
s=ut+1/2at^2(u=0again)
as it is released, not pushed
s=1/2x1.67x41.2^2
s=1420m
therefor the position is 1420m east from original point

i hope i didnt think wrong
參考: myself


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