I. A dart player throws a dart horizontally at a speed of 12.4 m/s. The dart hits the board 0.32 m below the height from which it was thrown. a. Draw the vector diagram, Label dx, dy, Vx, Vyf, b. How much time is the dart in the air? Show Your Work: Your answer: 2pts include the unit_ 2009 mark du toit www.macon.co.uk
I. A dart player throws a dart horizontally at a speed of 12.4 m/s. The dart hits the board 0.32 m below the height from which it was thrown. a. Draw the vector diagram, Label dx, dy, Vx, Vyf, b. How much time is the dart in the air? Show Your Work: Your answer: 2pts include the unit_ 2009 mark du toit www.macon.co.uk
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![### Projectile Motion Problem
A dart player throws a dart horizontally at a speed of 12.4 m/s. The dart hits the board 0.32 m below the height from which it was thrown.
#### Part a. Vector Diagram
**Task:** Draw the vector diagram. Label \( d_x \), \( d_y \), \( v_x \), and \( v_y \).
*Illustration:* There is an image showing a cartoon character throwing a dart horizontally towards a dartboard. The trajectory of the dart is displayed with several positions of the dart marked, indicating its path. Key variables such as the horizontal and vertical distances (\( d_x \), \( d_y \)) and velocities (\( v_x \), \( v_y \)) should be labeled in this context.
#### Part b. Time of Flight
**Question:** How much time is the dart in the air?
**Instructions:** Show Your Work
\[ \text{Your answer (2 points): Include the unit} \_\_\_\_\_\_\_\_\_\_\_\_ \]
#### Part c. Horizontal Distance
**Question:** How far away is the player from the board?
**Instructions:** Show Your Work
\[ \text{Your answer (3 points): Include the unit} \_\_\_\_\_\_\_\_\_\_\_\_ \]
### Explanation
1. **Vector Diagram:**
- \( d_x \): Horizontal distance from the throwing point to the board.
- \( d_y \): Vertical distance from the throwing height to the board (0.32 m).
- \( v_x \): Initial horizontal velocity (12.4 m/s).
- \( v_y \): Final vertical velocity.
2. **Time of Flight Calculation:**
- Using the equation of motion under gravity for vertical displacement:
\[
d_y = \frac{1}{2} g t^2
\]
Given \( d_y = 0.32 \) m and \( g = 9.8 \) m/s², solve for \( t \).
3. **Horizontal Distance Calculation:**
- Use the time of flight \( t \) found in part b:
\[
d_x = v_x \times t
\]
Given \( v_x = 12.4 \) m/s, solve for \( d_x \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3f0a09bd-ef71-43b6-abcd-653755da1dfb%2F28ea5f6a-0a1b-42da-800e-08e2a13e45ec%2F2pfi4fh_processed.png&w=3840&q=75)
Transcribed Image Text:### Projectile Motion Problem
A dart player throws a dart horizontally at a speed of 12.4 m/s. The dart hits the board 0.32 m below the height from which it was thrown.
#### Part a. Vector Diagram
**Task:** Draw the vector diagram. Label \( d_x \), \( d_y \), \( v_x \), and \( v_y \).
*Illustration:* There is an image showing a cartoon character throwing a dart horizontally towards a dartboard. The trajectory of the dart is displayed with several positions of the dart marked, indicating its path. Key variables such as the horizontal and vertical distances (\( d_x \), \( d_y \)) and velocities (\( v_x \), \( v_y \)) should be labeled in this context.
#### Part b. Time of Flight
**Question:** How much time is the dart in the air?
**Instructions:** Show Your Work
\[ \text{Your answer (2 points): Include the unit} \_\_\_\_\_\_\_\_\_\_\_\_ \]
#### Part c. Horizontal Distance
**Question:** How far away is the player from the board?
**Instructions:** Show Your Work
\[ \text{Your answer (3 points): Include the unit} \_\_\_\_\_\_\_\_\_\_\_\_ \]
### Explanation
1. **Vector Diagram:**
- \( d_x \): Horizontal distance from the throwing point to the board.
- \( d_y \): Vertical distance from the throwing height to the board (0.32 m).
- \( v_x \): Initial horizontal velocity (12.4 m/s).
- \( v_y \): Final vertical velocity.
2. **Time of Flight Calculation:**
- Using the equation of motion under gravity for vertical displacement:
\[
d_y = \frac{1}{2} g t^2
\]
Given \( d_y = 0.32 \) m and \( g = 9.8 \) m/s², solve for \( t \).
3. **Horizontal Distance Calculation:**
- Use the time of flight \( t \) found in part b:
\[
d_x = v_x \times t
\]
Given \( v_x = 12.4 \) m/s, solve for \( d_x \).
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