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Chapter 2: Problem 96

You are trying to improve your shooting skills by shooting at a can on top of a fence post. You miss the can, and the bullet, moving at \(200 . \mathrm{m} / \mathrm{s},\) is embedded \(1.5 \mathrm{~cm}\) into the post when it comes to a stop. If constant acceleration is assumed, how long does it take for the bullet to stop?

Short Answer

Expert verified
Answer: It takes approximately 0.00075 seconds for the bullet to stop after hitting the fence post.

Step by step solution

01

Identify the equations of motion

We can use the following equation of motion to solve for the time it takes the bullet to stop: v = u + a*t where: - v is the final velocity (0 m/s, since the bullet stops) - u is the initial velocity (200 m/s) - a is the acceleration - t is the time we want to find. But first, we need to find the constant acceleration (a). We can use the equation: v^2 = u^2 + 2*a*s where: - s is the distance the bullet travels into the post (0.015 m).
02

Calculate the constant acceleration

Using the second equation, v^2 = u^2 + 2*a*s, and given values, we get: 0^2 = 200^2 + 2*a*0.015 Solve for a: a = -(200^2) / (2*0.015) a = -266666.67 m/s²
03

Calculate the time it takes for the bullet to stop

Now, we'll use the first equation of motion, v = u + a*t, to find the time it takes the bullet to stop: 0 = 200 + (-266666.67)*t Solve for t: t = -200 / -266666.67 t = 0.00075 s So, it takes approximately 0.00075 seconds for the bullet to stop after hitting the fence post.

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Most popular questions from this chapter

An F-14 Tomcat fighter jet is taking off from the deck of the USS Nimitz aircraft carrier with the assistance of a steam-powered catapult. The jet's location along the flight deck is measured at intervals of \(0.20 \mathrm{~s} .\) These measurements are tabulated as follows: $$ \begin{array}{|l|l|l|l|l|l|l|l|l|l|l|l|} \hline t(\mathrm{~s}) & 0.00 & 0.20 & 0.40 & 0.60 & 0.80 & 1.00 & 1.20 & 1.40 & 1.60 & 1.80 & 2.00 \\ \hline x(\mathrm{~m}) & 0.0 & 0.70 & 3.0 & 6.6 & 11.8 & 18.5 & 26.6 & 36.2 & 47.3 & 59.9 & 73.9 \\ \hline \end{array} $$ Use difference formulas to calculate the jet's average velocity and average acceleration for each time interval. After completing this analysis, can you say if the F- 14 Tomcat accelerated with approximately constant acceleration?

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