An errand of Mercy. An airplane is dropping bales of hay to cattle stranded in a

Question

An errand of Mercy. An airplane is dropping bales of hay to cattle stranded in a blizzard on the Great Plains. The pilot releases the bales at 150m above the level ground when the
plane is flying at 75m/s in a direction 55 degrees above the horizontal(the plane is gaining altitude).

a) How far in front of the cattle should the pilot release the hay so that the bales land at the point where the cattle are stranded?

b) Suppose the above speed is air speed, and not with respect to the ground. Further suppose that there is a cross-wind of speed 40 mph(miles per hours. Your compass
says that you're going north, while the weather service reports the winds are coming out of the east. How (and how much) does this change the release point of the hay?

I NEED HELP WITH QUESTION B, THANKS.

Explanation / Answer

(A) in vertical,

yi = 150 m

v0y = 75 sin55 = 61.4 m/s

ay = - 9.8 m/s^2

yf - yi = v0y t + ay t^2 / 2

0 - 150 = 61.4 t - 9.8 t^2 /2

t = 14.62 s

In horizontal,

d = (V0x) t = ( 75 cos55)(14.62)

d = 629 m

(B) v_air = 40 x 1609 m / 3600s = 17.9 m/s

now new v_x = sqrt((75cos55)^2 + 17.9^2)

v_x = 46.6 m/s

d' = (46.6)(14.62) = 681.3 m

delta(d) = d' - d= 52.3 m

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