Chapter 2: Problem 16

An archer aims an arrow precisely horizontally over a large, flat field and lets it fly. 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

Answer: The watch and the arrow will hit the ground at the same time.

Step by step solution

Identify the given information and what we need to find

We are given that the archer aims the arrow horizontally, and both the watch and the arrow fall from the same height. We need to find whether the watch and the arrow hit the ground at the same time, before, or after each other.

Remember the free-fall motion's equations

The key equation for the free-fall motion is the equation relating the vertical displacement (h), initial vertical velocity (v0), acceleration due to gravity (g), and time (t): h = v0*t + (1/2)*g*t^2

Analyze the motion of the watch

The watch falls straight down with an initial vertical velocity (v0) of 0. The only force acting on it is gravity, with acceleration (g) of approximately -9.81 m/s^2. We can use the free-fall equation to determine the time it takes for the watch to hit the ground: h = 0*t + (1/2)*(-9.81)*t^2

Analyze the motion of the arrow

The arrow is shot horizontally, so its initial vertical velocity (v0) is also 0. Again, the only force acting on it is gravity, with acceleration (g) of approximately -9.81 m/s^2. We can use the same free-fall equation as for the watch: h = 0*t + (1/2)*(-9.81)*t^2

Compare the equations and draw a conclusion

Since both the watch and the arrow have the same initial vertical velocity (v0) and gravitational acceleration (g), the equations we derived are the same. This means that both objects fall with the same vertical motion, and thus, hit the ground at the same time. So the watch and the arrow will hit the ground at the same time.

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An archer aims an arrow precisely horizontally over a large, flat field and lets it fly. 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

Step by step solution

Identify the given information and what we need to find

Remember the free-fall motion's equations

Analyze the motion of the watch

Analyze the motion of the arrow

Compare the equations and draw a conclusion

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