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Chapter 2: Problem 16

An archer aims an arrow exactly horizontal over a flat field and shoots it. At the same instant, the archer's watchband breaks and the watch falls to the ground. Does the watch hit the ground before, at the same time as, or after the arrow hits the ground? Defend your answer.

Short Answer

Expert verified
A: The watch and the arrow hit the ground at the same time.

Step by step solution

01

Analyze the paths of the arrow and the watch

In this problem, the arrow is shot horizontally and the watch falls vertically. They both are initially at the same height from the ground, and the same gravitational force acts upon them.
02

Calculate the time it takes for the arrow and watch to hit the ground

We will calculate the time it takes for both the arrow and watch to hit the ground using the vertical motion equation: y = y0 + v0y * t - 0.5 * g * t² where y = 0 (Both hit the ground) y0 = initial height from the ground (same for both) v0y = initial vertical velocity (0 for both, as they start from rest) g = acceleration due to gravity (approximately 9.81 m/s^2) t = time it takes to hit the ground Since both the arrow and watch are accelerating due to gravity, we can use this equation to find the time it takes for both to hit the ground. Note that since the initial vertical velocities are 0, the equation simplifies to: y = y0 - 0.5 * g * t² --> t = sqrt(2 * y0 / g)
03

Compare the time it takes for the arrow and watch to hit the ground

Since both the arrow and the watch have the same initial height and are both acted upon by the same gravitational force, they will hit the ground at the same time. In conclusion, the watch and the arrow hit the ground at the same time.

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