A relief airplane is delivering a food package to a group of people stranded on

Question

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 452km/hour at an altitude of 625m . 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 acceleration due to gravity is g = 9.80m/s2.

Part A

After a package is ejected from the plane, how long will it take for it to reach sea level from the time it is ejected? Assume that the package, like the plane, has an initial velocity of 452km/hour in the horizontal direction. ( neglect air resistance)

Part B

If the package is to land right on the island, at what horizontal distance D from the plane to the island should the package be released?

Express the distance numerically in meters.

Part C

What is the speed vf of the package when it hits the ground?

Express your answer numerically in meters per second.

Explanation / Answer

Part A:

All that matters here is the height from which the package is dropped. The formula is:

x = vit + 1/2at^2
625 = 0 * t + 1/2 * 9.8 * t^2
625 = 4.9 * t^2
t^2 = 127.55
t = 11.29 s

11.29 s

Part B:

First of all, convert mph into meters per second. Mastering Physics will constantly try and catch you with trick questions like this. Be very careful of units. 452 km/hr = 125.56 m/s.

Now, since the package will be falling for 11.29 seconds and we know the velocity is 125.56 m/s, just use the formula x = vit + 1/2at2. There is no horizontal acceleration because we ignore air resistance:

x = vit + 1/2at2
x = 125.56 * 11.29 + 1/2 * 0 * 11.29^2
x = 1481.30 m

1481.30 m

Part C:

We need both the x and y components of the velocity to solve this part. Since we

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