a package of supplies is to be dropped from an airplane so that it hits the ground at a designated spot near some campers. The airplane, moving horizontally at a constant velocity of 140 km/hr, approaches the spot at an altitude of 0.5 km above level ground. Having the designated point in sight, the pilot prepares to drop the package. what should the angle be between the horizontal and the pilot's line of sight when the package is released?

Question

anonymous · Answer

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the time it takes for the package to reach down to ground from 1/2 km height is:
1/2=1/2gt^2
1=gt^2
$$t=\sqrt(g)$$
t=3.13 seconds

how much the airplane covers in x-axes during that time, u've got the speed 38.8 m/s
x=vt
x=(38.8)(3.13)=121.5 m

now u know the height, and the horizontal distance, using trigo, u can find the angel:

$$cos\theta=x/h$$
$$\theta=cos^{-1}(121.5/500)$$
$$\theta=75.93$$