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

254.56 m

Step-by-step 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=(1)/(2)gt^(2)\\160=(1)/(2)*10* t^(2)\\t=√(32)=4√(2)\text{ }sec`

So, in this time, the supply moves a horizontal distance of
`(4√(2)\text{ }sec)*(45\text{ }(m)/(sec))=180√(2)\text{ }m=254.56\text{ }m`.

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