Thank you for visiting At a shooting gallery a man fires a bullet from a rifle horizontally at a target The target is 75 00 m away The bullet. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
Sure! Let's work through the problem step by step.
### Part (a): Calculate the time it takes for the bullet to hit the target
1. Identify the information given:
- The distance to the target is 75.00 meters.
- The speed of the bullet is 150.0 meters per second.
2. Use the formula for time:
- Since the bullet travels horizontally, the time [tex]\( t \)[/tex] it takes to reach the target is based on the horizontal motion formula:
[tex]\[
\text{time} = \frac{\text{distance}}{\text{speed}}
\][/tex]
3. Plug in the values:
[tex]\[
t = \frac{75.00 \text{ m}}{150.0 \text{ m/s}} = 0.50 \text{ seconds}
\][/tex]
So, the bullet takes 0.50 seconds to hit the target.
### Part (b): Show that the bullet hits the target 1.25 m below the horizontal
1. Use the vertical motion equation:
- Since the bullet is fired horizontally, its initial vertical velocity ([tex]\( u \)[/tex]) is 0.
- We are given that [tex]\( g = 10 \, \text{m/s}^2 \)[/tex].
- The formula for vertical displacement ([tex]\( s \)[/tex]) when the initial velocity is 0 is:
[tex]\[
s = 0.5 \times g \times t^2
\][/tex]
2. Substitute the known values:
- Use the time [tex]\( t = 0.50 \)[/tex] seconds we found in part (a):
[tex]\[
s = 0.5 \times 10 \, \text{m/s}^2 \times (0.50 \, \text{s})^2
\][/tex]
3. Calculate the displacement:
[tex]\[
s = 0.5 \times 10 \times 0.25 = 1.25 \text{ m}
\][/tex]
Therefore, the bullet hits the target 1.25 meters below the horizontal.
### Part (a): Calculate the time it takes for the bullet to hit the target
1. Identify the information given:
- The distance to the target is 75.00 meters.
- The speed of the bullet is 150.0 meters per second.
2. Use the formula for time:
- Since the bullet travels horizontally, the time [tex]\( t \)[/tex] it takes to reach the target is based on the horizontal motion formula:
[tex]\[
\text{time} = \frac{\text{distance}}{\text{speed}}
\][/tex]
3. Plug in the values:
[tex]\[
t = \frac{75.00 \text{ m}}{150.0 \text{ m/s}} = 0.50 \text{ seconds}
\][/tex]
So, the bullet takes 0.50 seconds to hit the target.
### Part (b): Show that the bullet hits the target 1.25 m below the horizontal
1. Use the vertical motion equation:
- Since the bullet is fired horizontally, its initial vertical velocity ([tex]\( u \)[/tex]) is 0.
- We are given that [tex]\( g = 10 \, \text{m/s}^2 \)[/tex].
- The formula for vertical displacement ([tex]\( s \)[/tex]) when the initial velocity is 0 is:
[tex]\[
s = 0.5 \times g \times t^2
\][/tex]
2. Substitute the known values:
- Use the time [tex]\( t = 0.50 \)[/tex] seconds we found in part (a):
[tex]\[
s = 0.5 \times 10 \, \text{m/s}^2 \times (0.50 \, \text{s})^2
\][/tex]
3. Calculate the displacement:
[tex]\[
s = 0.5 \times 10 \times 0.25 = 1.25 \text{ m}
\][/tex]
Therefore, the bullet hits the target 1.25 meters below the horizontal.
Thank you for reading the article At a shooting gallery a man fires a bullet from a rifle horizontally at a target The target is 75 00 m away The bullet. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
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Rewritten by : Jeany
