# 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)...

See similar textbooks

Similar questions

In 2000, NASA placed a satellite in orbit around an asteroid. Consider a spherical asteroid with a mass of 1.40×1016 kg and a radius of 8.20 km What is the speed of a satellite orbiting 4.90 km above the surface? What is the escape speed from the asteroid?
Two planets of equal mass orbit a much more massive star. Planet m 1 moves in a circular orbit of radius r 1 = 10^11 m with a period of 2 years (= 6.3 x 10^7 s). Planet m 2 moves in an elliptical orbit with its closes t distance r 1 and its farthest distance r 2 = 1.8 x 10^11 m. a. Find the period of m 2’s orbit. b. The elliptical orbit has greater energy. Which planet has the greater potential energy at point P? Justify. c. Which planet has the greater speed at point P? Justify. d. How does the speed of m 2 at point P compare with the speed at point A? Justify.
Jupiter's moon Io has active volcanoes (in fact, it is the most volcanically active body in the solar system) that eject material as high as 500 km (or even higher) above the surface. Io has a mass of 8.93×1022kg8.93×1022kg and a radius of 1821 km. How high would this material go on earth if it were ejected with the same speed as on Io? (RE = 6370 km, mE=5.96×1024kg)
The radius Rh of a black hole is the radius of a mathematical sphere, called the event horizon, that is centered on the black hole. Information from events inside the event horizon cannot reach the outside world. According to Einstein's general theory of relativity, Rh = 2GM/c2, where M is the mass of the black hole and c is the speed of light. Suppose that you wish to study a black hole near it, at a radial distance of 48Rh. However, you do not want the difference in gravitational acceleration between your feet and your head to exceed 10 m/s2 when you are feet down (or head down) toward the black hole. (a) Take your height to be 1.5 m. What is the limit to the mass of the black hole you can tolerate at the given radial distance? Give the ratio of this mass to the mass MS of our Sun.
In 2000 , NASA placed a satellite in orbit around an asteroid. consider a spherical asteroid with a mass of 1.50 * 10^16 kg and a radius of 10.0 km what is the speed of a satellitie orbiting 5.90 km above the surface ? express with appropriate units what is the escape speed from the asteroid (express with appropriate units)
Consider the gravitational acceleration on the surface of the Moon and of Mars. a) What is the acceleration, in meters per square second, due to gravity on the surface of the Moon? You will need to look up the mass and radius of the Moon. b) What is the acceleration, in meters per square second, due to gravity on the surface of Mars? The mass of Mars is 6.418 × 1023 kg and its radius is 3.38 × 106 m. Given: the radius of the moon is 1,080 miles
You are visiting a newly discovered exoplanet (mass M and radius R) that completes one rotation about its axis every 12 hours (Earth hours). You place your spaceship in a geostationary orbit at an altitude h = 6R above the planet's surface. While in orbit you decided to beam down to the planet to investigate the surface. While on the surface you perform a simple kinematics experiment and discover that the gravitational acceleration at the surface is ap = 0.60g, where g is the gravitational acceleration on the Earth's surface. You can assume that the exoplanet is a uniform sphere, and that your spaceship's orbit is circular. Note: A geostationary orbit is a special type of geosynchronous orbit where the satellite/spaceship remains at the same position above the equator throughout its orbit. Technically the prefix "geo" indicates the Earth, but we'll go ahead and use the term here in reference to this new planet. (a) What is the radius of the planet? R = km (b) What is the mass of the…
An undiscovered planet, many lightyears from Earth, has one moon in a periodic orbit. This moon takes 1810 × 103 seconds (about 21 days) on average to complete one nearly circular revolution around the unnamed planet. If the distance from the center of the moon to the surface of the planet is 255.0 × 106 m and the planet has a radius of 3.30 × 106 m, calculate the moon's radial acceleration ?cac.
At the surface of planet X, a 1 kg object weighs 4 N (planet radius R=106m). A space probe passes by planet X with the nearest point (A) at 8R from the center. When the probe was very far away it had a speed of sqrt(2gxR), where gx is the acceleration of gravity at the planet surface. Find a value for the speed of this probe when it is at point A, vA.
A satellite is traveling around a planet in a circular orbit with radius R. It moves in a constant speed of v = 1.02 × 104 m/s. The mass of the planet is M = 5.94 × 1024 kg. The mass of the satellite is m = 4.7 × 103 kg. Enter an expression for the magnitude of the gravitional force F in terms of M,R,m and the gravitional constant G. Enter an expression for the radius in terms of G,M and R. Enter an expression for the gravational potetial energy PE in terms of G,M,m and R. Enter an expresssion for the centripal acceleration of the satellite ac in terms of the speed of the satellite v, and r.
An object of mass m is launched from a planet of mass M and radius R. a)Derive and enter an expression for the minimum launch speed needed for the object to escape gravity, i.e. to be able to just reach r = ∞. b)Calculate this minimum launch speed (called the escape speed), in meters per second, for a planet of mass M = 6 × 1023 kg and R = 76 × 104 km.
(D Page view A Read aloud V Draw y Highlight Erase