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Chapter 3: Problem 82

An African swallow carrying a very small coconut is flying horizontally with a speed of \(18 \mathrm{m} / \mathrm{s}\). (a) If it drops the coconut from a height of \(100 \mathrm{m}\) above the Earth, how long will it take before the coconut strikes the ground? (b) At what horizontal distance from the release point will the coconut strike the ground?

Short Answer

Expert verified
Question: A coconut is dropped from a height of 100 meters by an African swallow flying horizontally with a speed of 18 m/s. Find (a) the time it takes before the coconut strikes the ground, and (b) the horizontal distance from the release point to where the coconut strikes the ground. Answer: (a) The time it takes before the coconut strikes the ground is approximately \(4.52 \thinspace s\). (b) The horizontal distance from the release point to where the coconut strikes the ground is approximately \(81.4 \thinspace m\).

Step by step solution

01

List the known values

For the given problem, we have the following known values: - Initial horizontal velocity, \(v_x = 18 \thinspace m/s\) - Vertical distance dropped, \(h = 100 \thinspace m\) - Acceleration due to gravity, \(g = 9.8 \thinspace m/s^2\)
02

Find the time it takes for the coconut to hit the ground

From the vertical motion, we can use the formula: \( h = v_{0y} t + \frac{1}{2}gt^2 \) Here, \(v_{0y}\) is the initial vertical velocity, which is zero. So, the equation simplifies to: \( h = \frac{1}{2}gt^2 \) Now, we can solve for t: \( t = \sqrt{\frac{2h}{g}} \) Substitute the given values of h and g: \( t = \sqrt{\frac{2 \times 100}{9.8}} \approx 4.52 \thinspace s \)
03

Find the horizontal distance the coconut travels before hitting the ground

Now that we have the time t it takes for the coconut to hit the ground, we can find the horizontal distance d it travels using the horizontal velocity: \( d = v_x t \) Substitute the given values for \(v_x\) and the value of t we found earlier: \( d = 18 \times 4.52 \approx 81.4 \thinspace m \)
04

Write the final answer

(a) The time it takes before the coconut strikes the ground is approximately \(4.52 \thinspace s\). (b) The horizontal distance from the release point to where the coconut strikes the ground is approximately \(81.4 \thinspace m\).

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