# Physics

A Coast Guard airplane needs to drop a rescue package to a ship floating adrift in the ocean. The plane flies 55 m above the ocean at a speed of 215 km/h. How far away from the ship should the crew drop the package out of the plane so that the package hits the water close to the ship?

1. 👍 0
2. 👎 0
3. 👁 412
1. The time it will take the package to hit the ocean is T = sqrt (2H/g), where H = 55 m and g is the acceleration of gravity, 9.8 m/s^2. T = 3.35 s.

Make sure that the package is dropped a distance X ahead of the target so that

X = V T

where V is the airplane's speed in m/s.

1. 👍 0
2. 👎 0
2. Alternatively:

Envision the airplane on a rescue run flying at a constant altitude "s" and with constant horizontal velocity "Vh". The objective target "O" is being observed by the pilot. When should the crew release the rescue package in order to hit the target? More specifically, at what angle to the vertical should the crew release the package?

Note that when the package is released, it retains the forward velocity of the airplane. Therefore, the package travels horizontally with a constant velocity independently of the simulaneous accelerated motion toward the earth's surface. As a result, the package will strike a point on the surface well ahead of the airplane's position at the time of release. The horizontal distance ahead of the airplane, "x", will make an angle "ø" with the vertical. Having "s", the altitude of the airplane, "x", the horizontal distance from the local vertical to the target objective "O", and "t", the time from release to the target, we have s = gt^2/2, x = Vh(t) and x = s(tanø), combining these expressions to eliminate both "x" and "t", we derive tanø = Vhsqrt(2/gs). Therefore, the crew releases the package when the pilot's instruements indicate that the angle from his local vertical position to the target is ø = arctan[Vh(sqrt(2/gs))].

Having ø, the horizontal distance from the target, at which the package should be relaeased, derives from x = stanø.

1. 👍 0
2. 👎 0

## Similar Questions

1. ### Physics

An Alaskan rescue plane drops a package of emergency rations to a stranded party of explorers. The plane is traveling horizontally at 40.0 m/s at a height of 100 m above the ground. a) How far horizontally from the dropping point

2. ### Physics

PLEASE HELP! A person throws a rock horizontally off a cliff ata a speed of 9 m/s from a point 64.8 m above the ground. How long is the rock in the air? 13.2 s 26.4 s 3.64 s(my guess) 5.14 s A package falls from an airplane in

3. ### Physics

help. A rescue helicopter drops a package of emergency ration to a stranded party on the ground. If the helicopter is traveling horizontally at 40m/sec at a height of 100 m above the ground, where does the package strike the

4. ### physics

A supply plane needs to drop a package of food to scientists working on a glacier in Greenland. The plane flies 92 m above the glacier at a speed of 135 m/s. How far short of the target should it drop the package?

1. ### math

A Coast Guard ship patrols an area of 125 square miles. The area the ship patrols is a square. About how long is each side of the square? Round your answer to the nearest mile.

2. ### Physics

A rescue plane spots a person floating in a lifeboat 55 m directly below and releases an emergency kit with a parachute. The package descends with a constant vertical acceleration of 6.91 m/s. If the horizontal speed of the plane

3. ### physics

a coast guard ship is traveling at a constant velocity of 4.20m/s, due east, relative to the water. on his radar screen the navigator detects an object that is moving at a constant velocity. the object is located at a distance of

4. ### Physics

An Alaskan rescue plane drops a package of emergency rations to a stranded party of explorers, as illustrated below in Figure 18. The plane is traveling horizontally at 30m/s at a height of 200m above the ground. a. What

1. ### algebra

A coast guard ship patrols an area of 125 square miles. If the area the ship patrols is a square, about how long is each side of the area? Round to the nearest mile.

2. ### Physics

An airplane dropping supplies to northern villages that are isolated by severe blizzards and cannot be reached by land vehicles. The airplane is flying at an altitude of 785m and at a constant horizontal velocity of 53.5 m/s. At

3. ### PHYSIC 220

A radar station locates a sinking ship at range 16.7 km and bearing 136° clockwise from north. From the same station, a rescue plane is at horizontal range 19.6 km, 153° clockwise from north, with elevation 2.40 km. (a) Write

4. ### Trigonometry

a) The ship left the port and sailed for 2 hours on a course of 75O, at an average speed of 2.5 nautical miles per hour. b) North It changed its course to 165O and travelled for 3 hours, at an average speed of 4 nautical miles per