# Educational Content: Physics Problem on Miranda, a Satellite of Uranus## Miranda, a Satellite of UranusMiranda, a satellite of Uranus, is depicted in part (a) of the figure below. It can be modeled as a sphere with a radius of 242 km and a mass of \(6.68 \times 10^{19}\) kg.### Figure Description**Part (a):** Image of Miranda, showing surface features for reference.**Part (b):** Enlarged image of a specific region on Miranda, illustrating a vertical cliff.### Problem Breakdown#### Question (a): Free-Fall Acceleration**Objective:** Determine the free-fall acceleration on Miranda's surface.**Given Values:** - Radius (\(r\)) = 242 km - Mass (\(m\)) = \(6.68 \times 10^{19}\) kg**Result:**\[ \text{Free-fall acceleration} = 0.076 \, \text{m/s}^2 \]#### Question (b): Time of Flight from a Cliff**Scenario:** A cliff on Miranda is 5.00 km high. An object is projected horizontally off the cliff at 5.50 m/s.**Task:** Calculate the time interval (\(t\)) of flight, ignoring gravitational change over the height of the cliff.**Given Values:**- Height (\(h\)) = 5.00 km- Initial horizontal velocity (\(v_x\)) = 5.50 m/s**Result:**\[ t = 362.74 \, \text{s} \]#### Question (c): Distance from the Cliff Base**Scenario:** The same object from part (b).**Task:** Determine the horizontal distance from the base of the cliff where the object strikes Miranda's surface.**Given Values:**- Time of flight (\(t\)) from part (b) = 362.74 s- Horizontal velocity (\(v_x\)) = 5.50 m/s**Result:**\[ \text{Distance} = 1995.06 \, \text{m} \]#### Question (d): Vector Impact Velocity**Scenario:** The same object as it impacts the surface of Miranda.**Task:** Calculate the vector magnitude of the impact velocity.**Results:**- Incorrect attempt: \( v = 27.

Answered: Image /qna-images/answer/61e1b92b-6633-4ba1-b12f-caf9adde2708.jpg

Miranda, a satellite of Uranus, is shown in part a of the figure below. It can be modeled as a sphere of radius 242 km and mass 6.68 x 101⁹ kg. (a) Find the free-fall acceleration on its surface. 0.076 ✔ m/s² (b) A cliff on Miranda is 5.00 km high. It appears on the limb at the 11 o'clock position in part a of the figure above and is magnified in part (b) of the figure above. A devotee of extreme sports runs horizontally off the top of the cliff at 5.50 m/s. For what time interval is he in flight? (Ignore the difference in g between the lip and base of the cliff.) 362.74 ✔ S (c) How far from the base of the vertical cliff does he strike the icy surface of Miranda? 1995.06 ✔ m (d) What is his vector impact velocity? 27.8 ✔m/s 28.11 x Your response differs from the correct answer by more than 10%. Double check your calculations. below the horizontal

Miranda, a satellite of Uranus, is shown in part a of the figure below. It can be modeled as a sphere of radius 242 km and mass 6.68 x 101⁹ kg. (a) Find the free-fall acceleration on its surface. 0.076 ✔ m/s² (b) A cliff on Miranda is 5.00 km high. It appears on the limb at the 11 o'clock position in part a of the figure above and is magnified in part (b) of the figure above. A devotee of extreme sports runs horizontally off the top of the cliff at 5.50 m/s. For what time interval is he in flight? (Ignore the difference in g between the lip and base of the cliff.) 362.74 ✔ S (c) How far from the base of the vertical cliff does he strike the icy surface of Miranda? 1995.06 ✔ m (d) What is his vector impact velocity? 27.8 ✔m/s 28.11 x Your response differs from the correct answer by more than 10%. Double check your calculations. below the horizontal

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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# Educational Content: Physics Problem on Miranda, a Satellite of Uranus

## Miranda, a Satellite of Uranus

Miranda, a satellite of Uranus, is depicted in part (a) of the figure below. It can be modeled as a sphere with a radius of 242 km and a mass of \(6.68 \times 10^{19}\) kg.

### Figure Description

**Part (a):** Image of Miranda, showing surface features for reference.

**Part (b):** Enlarged image of a specific region on Miranda, illustrating a vertical cliff.

### Problem Breakdown

#### Question (a): Free-Fall Acceleration
**Objective:** Determine the free-fall acceleration on Miranda's surface.

**Given Values:**
- Radius (\(r\)) = 242 km
- Mass (\(m\)) = \(6.68 \times 10^{19}\) kg

**Result:**
\[ \text{Free-fall acceleration} = 0.076 \, \text{m/s}^2 \]

#### Question (b): Time of Flight from a Cliff
**Scenario:** A cliff on Miranda is 5.00 km high. An object is projected horizontally off the cliff at 5.50 m/s.

**Task:** Calculate the time interval (\(t\)) of flight, ignoring gravitational change over the height of the cliff.

**Given Values:**
- Height (\(h\)) = 5.00 km
- Initial horizontal velocity (\(v_x\)) = 5.50 m/s

**Result:**
\[ t = 362.74 \, \text{s} \]

#### Question (c): Distance from the Cliff Base
**Scenario:** The same object from part (b).

**Task:** Determine the horizontal distance from the base of the cliff where the object strikes Miranda's surface.

**Given Values:**
- Time of flight (\(t\)) from part (b) = 362.74 s
- Horizontal velocity (\(v_x\)) = 5.50 m/s

**Result:**
\[ \text{Distance} = 1995.06 \, \text{m} \]

#### Question (d): Vector Impact Velocity
**Scenario:** The same object as it impacts the surface of Miranda.

**Task:** Calculate the vector magnitude of the impact velocity.

**Results:**
- Incorrect attempt: \( v = 27.

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