(Figure 1)A relief airplane is delivering a food package to...

(Figure 1)A relief airplane is delivering a food package to a group of people stranded on a very small island. The island is too small for the plane to land on, and the only way to deliver the package is by dropping it. The airplane flies horizontally with constant speed of 322 km/hour at an altitude of 875 m . The positive x and y directions are defined in the figure. For all parts, assume that the "island" refers to the point at a distance D from the point at which the package is released, as shown in the figure. Ignore the height of this point above sea level. Assume that the free-fall acceleration is g = 9.80 m/s² .

Transcript

00:01 In this video, we're going to be working with 2d kinematics, so motion in two dimensions.

00:06 Okay, what we have is an island in the middle of the ocean, okay, at y equals zero or sea level.

00:14 We have a plane coming in that's going to be dropping a relief package to the island.

00:20 Okay, the plane can't land on the island because it's too small, so it has to drop it.

00:25 We want to find how far away should the plane be d from the island when it drops the package in order so that the package will land on the island.

00:34 Okay, so the plane's going to drop the package somewhere over here, and it's going to travel like this in a parabolic path till it hits the island.

00:43 Right, so we want to find this distance, d, and we have some data to help us with that.

00:49 Okay, we have the velocity of the plane.

00:52 Okay, so i'll call that v -p.

00:54 V -p equals 422 kilometers, per hour and that equals 117 meters per second.

01:09 Okay, we have the altitude at which the plane flies.

01:13 Okay, so the distance above the ground.

01:16 I'll call that h.

01:17 H equals 625 meters.

01:24 Okay, and we can use this information to find d.

01:28 That's the horizontal distance.

01:30 The plane from the island where the plane's going to drop the package.

01:34 So from here to here.

01:36 And let me define a coordinate system.

01:38 So this is going to be, i'm going to call this positive x, positive y.

01:42 So h is going to be 625 meters positive y.

01:47 And velocity of the plane is 117 meters per second, the x direction.

01:54 So how do we approach this problem? first, i'm going to find the time that it takes the package to go from its initial release point to its final point at y equals zero.

02:07 And once i have that time, i'm going to use the expression d in the x direction equals d x times t...

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