Conservation of Energy, Projectile Motion, Acceleration x, y, z. A marble of weight=5lb is launch thanks to a spring on a ramp. The spring has a coefficient of rigidity of = 5lb/ft, an unstretched length of s0=7ft. The ramp is 1=9ft long and h=5ft tall. k www. е VA h Th max Range If the velocity at A is vA=9ft/s find: 1. The displacement of the spring needed to reach this velocity. 2. The range of the flight. 3. The maximum altitude of the flight. с In the box below, enter the maximum altitude of the flight in ft with 2 decimals (Question3).
Conservation of Energy, Projectile Motion, Acceleration x, y, z. A marble of weight=5lb is launch thanks to a spring on a ramp. The spring has a coefficient of rigidity of = 5lb/ft, an unstretched length of s0=7ft. The ramp is 1=9ft long and h=5ft tall. k www. е VA h Th max Range If the velocity at A is vA=9ft/s find: 1. The displacement of the spring needed to reach this velocity. 2. The range of the flight. 3. The maximum altitude of the flight. с In the box below, enter the maximum altitude of the flight in ft with 2 decimals (Question3).
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Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
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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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![**Conservation of Energy, Projectile Motion, Acceleration x, y, z**
A marble of weight = 5 lb is launched thanks to a spring on a ramp.
The spring has a coefficient of rigidity of k = 5 lb/ft, an unstretched length of s0 = 7 ft.
The ramp is l = 9 ft long and h = 5 ft tall.
![diagram]
In the diagram:
- A spring (denoted by the symbol K) is compressed and launches the marble up a ramp.
- The ramp is inclined and leads to point A, where the marble has a velocity \( v_A \).
- The point A is the beginning of the projectile motion path.
- The path from point A to point C shows the projectile trajectory of the marble with a parabolic shape.
- Point B represents the maximum altitude \( h_{\text{max}} \) of the marble’s flight.
- The horizontal distance from point A to point C is labeled as the Range.
**Given:**
If the velocity at A is \( v_A = 9 \) ft/s, find:
1. The displacement of the spring needed to reach this velocity.
2. The range of the flight.
3. The maximum altitude of the flight.
**Instructions for solving the problems:**
1. **Displacement of the Spring:**
- Use energy conservation principles to connect the spring displacement to the launch velocity \( v_A \).
2. **Range of the Flight:**
- Use projectile motion equations to find the range. This involves decomposing the launch velocity into horizontal and vertical components.
3. **Maximum Altitude of the Flight:**
- Use kinematic equations to find the maximum altitude.
**Example Equations:**
1. Spring Potential Energy: \( \frac{1}{2} k x^2 \)
2. Kinematic Equations for Projectile Motion.
3. Energy Conservation: Potential Energy of the Spring = Kinetic Energy at A.
**Input Instructions:**
In the box below, enter the maximum altitude of the flight in ft with 2 decimals (Question 3).
---
**Note on the Diagram:**
- The inclined plane (ramp) is marked with its length and height.
- The spring is shown compressed at the bottom of the ramp.
- The trajectory from A to C is a dashed curve, indicating the parabolic path of the projectile.
- Arrows and labels indicate key quantities to be calculated](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F697ee80b-6834-4809-8325-e33cf8ac2219%2F20c23299-8be4-4bdb-a874-0e79bfb3d124%2Fhmdb506_processed.png&w=3840&q=75)
Transcribed Image Text:**Conservation of Energy, Projectile Motion, Acceleration x, y, z**
A marble of weight = 5 lb is launched thanks to a spring on a ramp.
The spring has a coefficient of rigidity of k = 5 lb/ft, an unstretched length of s0 = 7 ft.
The ramp is l = 9 ft long and h = 5 ft tall.
![diagram]
In the diagram:
- A spring (denoted by the symbol K) is compressed and launches the marble up a ramp.
- The ramp is inclined and leads to point A, where the marble has a velocity \( v_A \).
- The point A is the beginning of the projectile motion path.
- The path from point A to point C shows the projectile trajectory of the marble with a parabolic shape.
- Point B represents the maximum altitude \( h_{\text{max}} \) of the marble’s flight.
- The horizontal distance from point A to point C is labeled as the Range.
**Given:**
If the velocity at A is \( v_A = 9 \) ft/s, find:
1. The displacement of the spring needed to reach this velocity.
2. The range of the flight.
3. The maximum altitude of the flight.
**Instructions for solving the problems:**
1. **Displacement of the Spring:**
- Use energy conservation principles to connect the spring displacement to the launch velocity \( v_A \).
2. **Range of the Flight:**
- Use projectile motion equations to find the range. This involves decomposing the launch velocity into horizontal and vertical components.
3. **Maximum Altitude of the Flight:**
- Use kinematic equations to find the maximum altitude.
**Example Equations:**
1. Spring Potential Energy: \( \frac{1}{2} k x^2 \)
2. Kinematic Equations for Projectile Motion.
3. Energy Conservation: Potential Energy of the Spring = Kinetic Energy at A.
**Input Instructions:**
In the box below, enter the maximum altitude of the flight in ft with 2 decimals (Question 3).
---
**Note on the Diagram:**
- The inclined plane (ramp) is marked with its length and height.
- The spring is shown compressed at the bottom of the ramp.
- The trajectory from A to C is a dashed curve, indicating the parabolic path of the projectile.
- Arrows and labels indicate key quantities to be calculated
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