Question

The pilot of an airplane traveling 45 m/s wants to drop supplies to flood victims isolated on a patch of land 160 m below. The supplies should be dropped when the plane is how many meters from the island?

Answer 1

Answer:

254.56 m

Explanation:

       A object dropped from a plane from a certain height will follow a parabolic trajectory because it has a horizontal velocity equal to plane's velocity.

       So, if supplies are to be dropped from a plane from a height of 160 m, let us calculate the time it takes to reach the ground.

       $H=\frac{1}{2}gt^{2}\\160=\frac{1}{2}\times10\times t^{2}\\t=\sqrt{32}=4\sqrt{2}\text{ }sec$

       So, in this time, the supply moves a horizontal distance of $(4\sqrt{2}\text{ }sec)\times(45\text{ }\frac{m}{sec})=180\sqrt{2}\text{ }m=254.56\text{ }m$.

∴ The supply must be dropped when the plane is 255 m away.