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 442km/hour at an altitude of 525m . 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 442km/hour in the horizontal direction. Express your answer numerically in seconds. Neglect air resistance. t = s SubmitHintsMy AnswersGive UpReview Part Incorrect; Try Again; 5 attempts remaining 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. D = m SubmitHintsMy AnswersGive UpReview Part Part C What is the speed vf of the package when it hits the ground? Express your answer numerically in meters per second. vf = m/s 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 442km/hour in the horizontal direction. 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? c) What is the speed vf of the package when it hits the ground?

Explanation / Answer

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 442 mph in the horizontal direction.
Express your answer numerically in seconds. Neglect air resistance.

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

x = vit + 1/2at2
525 = 0 * t + 1/2 * 9.8 * t2
525 = 4.9 * t2
t2 = 107.14
t = 10.35 s

10.35 s

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.

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. One mph = 0.44704 m/s, so 442 mph = 197.59 m/s.

Now, since the package will be falling for 10.35 seconds and we know the velocity is 442 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 = 197.59 * 10.35 + 1/2 * 0 * 10.35^2
x = 197.59 * 10.35
x = 2045 m

2045 m

Part C

What is the speed vf of the package when it hits the ground?
Express your answer numerically in miles per hour.

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

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