(b) Is the motion of the rock one with constant velocity or constant acceleration? Choose an appropriate equation of motion to calculate the height of the cliff. Something to think about: Do you need to split the trip into two parts: 1. the rock's journey up, and 2. the rock's journey down? Is it possible to solve without splitting the motion into two parts? Ay=vt Ay = (vo+ v)₁ t 2 v=v₁ + at ✓= √²+2aAy 1 Ay= Vot+2 -at² (c) Calculate the height of the cliff. Note: The height of the cliff should be a positive value. Enter to 3 significant figures h= t= m (d) How long would it take the rock to reach the ground if it is thrown straight down with the same speed instead of up? Enter to 3 significant figures S Sense-making: Check if the answer in part (d) is less than the time in part (a).

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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**Physics Problem on Motion**

**(b) Motion Analysis**
- Question: Is the motion of the rock characterized by constant velocity or constant acceleration?
- Selection: Use the dropdown menu to choose the correct type of motion.

**Equation Selection for Cliff Height Calculation**
- Task: Choose an appropriate equation of motion to determine the height of the cliff.
- **Consideration**: 
  - Do you need to divide the rock's motion into two phases: 1. the ascent, and 2. the descent?
  - Can the problem be solved without dividing the motion?

**Equations of Motion:**
1. \( \Delta y = vt \)
2. \( \Delta y = \frac{(v_0 + v)}{2} t \)
3. \( v = v_0 + at \)
4. \( v^2 = v_0^2 + 2a\Delta y \)
5. \( \Delta y = v_0 t + \frac{1}{2} at^2 \)

**(c) Height Calculation**
- Task: Compute the height of the cliff. The result should be positive.
- Input Format: Enter to 3 significant figures
  - \( h = \) [Input box] m

**(d) Time Calculation for Descent**
- Task: Calculate the time taken for the rock to hit the ground if it is thrown straight down with the same speed.
- Input Format: Enter to 3 significant figures
  - \( t = \) [Input box] s

**Sense-Making**
- Verify if the time calculated in part (d) is less than the time in part (a).
Transcribed Image Text:**Physics Problem on Motion** **(b) Motion Analysis** - Question: Is the motion of the rock characterized by constant velocity or constant acceleration? - Selection: Use the dropdown menu to choose the correct type of motion. **Equation Selection for Cliff Height Calculation** - Task: Choose an appropriate equation of motion to determine the height of the cliff. - **Consideration**: - Do you need to divide the rock's motion into two phases: 1. the ascent, and 2. the descent? - Can the problem be solved without dividing the motion? **Equations of Motion:** 1. \( \Delta y = vt \) 2. \( \Delta y = \frac{(v_0 + v)}{2} t \) 3. \( v = v_0 + at \) 4. \( v^2 = v_0^2 + 2a\Delta y \) 5. \( \Delta y = v_0 t + \frac{1}{2} at^2 \) **(c) Height Calculation** - Task: Compute the height of the cliff. The result should be positive. - Input Format: Enter to 3 significant figures - \( h = \) [Input box] m **(d) Time Calculation for Descent** - Task: Calculate the time taken for the rock to hit the ground if it is thrown straight down with the same speed. - Input Format: Enter to 3 significant figures - \( t = \) [Input box] s **Sense-Making** - Verify if the time calculated in part (d) is less than the time in part (a).
### Transcription and Explanation for Educational Website:

1. **Solution Overview**:
   The provided solution shows how Part 1 should have been structured using vectors to represent motion.

2. **Diagram Description**:
   - The diagram illustrates the motion of a rock thrown vertically from a cliff.
   - Vectors are shown for initial velocity \( v_0 \), final velocity \( v \), and acceleration \( a \).
   - The top of the cliff is labeled \( y_0 \), and the bottom of the cliff is marked as the end point for \( y \).

3. **Vector Orientation**:
   - \( v_0 \) (initial velocity) is directed upwards (blue arrow).
   - \( v \) (final velocity) is directed downwards (green arrow).
   - \( a \) (acceleration due to gravity) points downward (red arrow).

4. **Problem Context**:
   - It takes 2 seconds for the rock to hit the ground after being thrown with an initial velocity of 7.00 m/s.
   - Calculations should consider up to 3 significant figures.

5. **Instructions (Part a)**:
   - Use \(\Delta y = y - y_0\) for displacement.
   - Identify known and unknown quantities using the variables:
     - \( y \): Position after time \( t \)
     - \( y_0 \): Initial position
     - \( v \): Velocity after time \( t \)
     - \( v_0 \): Initial velocity
     - \( a \): Acceleration
   - Enter values for known quantities, ensuring vector signs match the diagram.

6. **Input Fields for Known Quantities**:
   - \( v_0 = \) [Enter value] m/s
   - \( a = \) [Enter value] m/s\(^2\)
   - \( t = \) [Enter value] s

This setup guides students through a physics problem involving projectile motion, emphasizing vector orientation and accurate calculation.
Transcribed Image Text:### Transcription and Explanation for Educational Website: 1. **Solution Overview**: The provided solution shows how Part 1 should have been structured using vectors to represent motion. 2. **Diagram Description**: - The diagram illustrates the motion of a rock thrown vertically from a cliff. - Vectors are shown for initial velocity \( v_0 \), final velocity \( v \), and acceleration \( a \). - The top of the cliff is labeled \( y_0 \), and the bottom of the cliff is marked as the end point for \( y \). 3. **Vector Orientation**: - \( v_0 \) (initial velocity) is directed upwards (blue arrow). - \( v \) (final velocity) is directed downwards (green arrow). - \( a \) (acceleration due to gravity) points downward (red arrow). 4. **Problem Context**: - It takes 2 seconds for the rock to hit the ground after being thrown with an initial velocity of 7.00 m/s. - Calculations should consider up to 3 significant figures. 5. **Instructions (Part a)**: - Use \(\Delta y = y - y_0\) for displacement. - Identify known and unknown quantities using the variables: - \( y \): Position after time \( t \) - \( y_0 \): Initial position - \( v \): Velocity after time \( t \) - \( v_0 \): Initial velocity - \( a \): Acceleration - Enter values for known quantities, ensuring vector signs match the diagram. 6. **Input Fields for Known Quantities**: - \( v_0 = \) [Enter value] m/s - \( a = \) [Enter value] m/s\(^2\) - \( t = \) [Enter value] s This setup guides students through a physics problem involving projectile motion, emphasizing vector orientation and accurate calculation.
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