Physics Fundamentals
2nd Edition
ISBN: 9780971313453
Author: Vincent P. Coletta
Publisher: PHYSICS CURRICULUM+INSTRUCT.INC.
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Chapter 6, Problem 11Q
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The asteroid 243 Ida has a mass of about 4.0×10^16 kg and an average radius of about 16 km (it's not spherical, but you can assume it is).
a) Calculate the speed with which you would have to throw a rock to put it into orbit around the asteroid 243 Ida, near the surface.
b) How long would it take for your rock to return and hit you in the back of the head?
We are planning a human exploration mission to Mars. We will first place our spacecraft into a circular around Mars and then send down a lander.
a) If we want the spacecraft to orbit at an altitude of 170 km above the Martian surface, what will the velocity and orbital period of the spacecraft?
b) When we land astronauts on the surface of Mars, what acceleration due to gravity in terms of g’s (i.e. as a fraction of the Earth’s gravitational acceleration) will the astronauts experience? You are permitted to use an online resource (e.g. Google) to find the necessary information about Mars that you might need in solving this problem.
You are on a space station, in a circular orbit h = 500 km above the surface of the Earth. You complete your tasks several days early and must wait for the next mission from the surface to bring you home. After days of boredom, you decide to play some golf. Walking on the space station surface with magnetic shoes, you tee up a golf ball. You hit it with all of your might, sending it off with speed υrel, relative to the space station, in a direction parallel to the velocity vector of the space station at the moment the ball is hit. You notice that you then orbit the Earth exactly n = 2.00 times and you reach up and catch the golf ball as it returns to the space station. With what speed υrel was the golf ball hit?
Chapter 6 Solutions
Physics Fundamentals
Ch. 6 - Prob. 1QCh. 6 - Prob. 2QCh. 6 - Prob. 3QCh. 6 - Prob. 4QCh. 6 - Prob. 5QCh. 6 - Prob. 6QCh. 6 - Prob. 7QCh. 6 - Prob. 8QCh. 6 - Prob. 9QCh. 6 - Prob. 10Q
Ch. 6 - Prob. 11QCh. 6 - Prob. 12QCh. 6 - Prob. 13QCh. 6 - Prob. 14QCh. 6 - Prob. 15QCh. 6 - Prob. 1PCh. 6 - Prob. 2PCh. 6 - Prob. 3PCh. 6 - Prob. 4PCh. 6 - Prob. 5PCh. 6 - Prob. 6PCh. 6 - Prob. 7PCh. 6 - Prob. 8PCh. 6 - Prob. 9PCh. 6 - Prob. 10PCh. 6 - Prob. 11PCh. 6 - Prob. 12PCh. 6 - Prob. 13PCh. 6 - Prob. 14PCh. 6 - Prob. 15PCh. 6 - Prob. 16PCh. 6 - Prob. 17PCh. 6 - Prob. 18PCh. 6 - Prob. 19PCh. 6 - Prob. 20PCh. 6 - Prob. 21PCh. 6 - Prob. 22PCh. 6 - Prob. 23PCh. 6 - Prob. 24PCh. 6 - Prob. 25PCh. 6 - Prob. 26PCh. 6 - Prob. 27PCh. 6 - Prob. 28PCh. 6 - Prob. 29PCh. 6 - Prob. 30PCh. 6 - Prob. 31PCh. 6 - Prob. 32PCh. 6 - Prob. 33PCh. 6 - Prob. 34PCh. 6 - Prob. 35PCh. 6 - Prob. 36PCh. 6 - Prob. 37PCh. 6 - Prob. 38PCh. 6 - Prob. 39PCh. 6 - Prob. 40PCh. 6 - Prob. 41PCh. 6 - Prob. 42PCh. 6 - Prob. 43PCh. 6 - Prob. 44PCh. 6 - Prob. 45P
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- In Example 2.6, we considered a simple model for a rocket launched from the surface of the Earth. A better expression for the rockets position measured from the center of the Earth is given by y(t)=(R3/2+3g2Rt)2/3j where R is the radius of the Earth (6.38 106 m) and g is the constant acceleration of an object in free fall near the Earths surface (9.81 m/s2). a. Derive expressions for vy(t) and ay(t). b. Plot y(t), vy(t), and ay(t). (A spreadsheet program would be helpful.) c. When will the rocket be at y=4R? d. What are vy and ay when y=4R?arrow_forwardAn inventor wants to launch small satellites into orbit by launching them straight up from the surface of the earth, at very high speeds. a) With what speed should he launch the satellite if it is to have a speed of 500 m/s at a height of 400 km? Ignore air resistance. b) By what percentage would your answer be in error if you used a flat earth approximation? y2 400 km r R, + y2 Vy= 500 ta/s After: y =0 km = R. Before: Re Eartharrow_forwardA rocket is projected upward from the earth's surface (r = RE) with an initial speed v0 that carries it to a distance r = 1.6 RE from the center of the earth. What is the launch speed v0? Assume that air friction can be ignored.arrow_forward
- The orbital speeds of the planets Mercury and Mars are v(Mercury) = 50 km / s and V(Mars) = 24.2 km / s. Assume that the orbits of these planets Mercury and Mars around the Sun are circular, find the ratio of the radii of their R (Mercury) / R (Mars) orbits.arrow_forwardA comet goes around the Sun in an elliptical orbit. At its farthest point, 600 million miles from the Sun, it is traveling with a speed of 15000 mi/h. How fast is it traveling at its closest approach to the Sun, at a distance of 100 million miles?arrow_forwardASAParrow_forward
- You are exploring a distant planet. When your spaceship is ina circular orbit at a distance of 630 km above the planet’s surface, the ship’sorbital speed is 4900 m/s. By observing the planet, you determine its radiusto be 4.48 * 10^6 m. You then land on the surface and, at a place where theground is level, launch a small projectile with initial speed 12.6 m>s at anangle of 30.8 above the horizontal. If resistance due to the planet’s atmosphereis negligible, what is the horizontal range of the projectile?arrow_forwardAn asteroid, headed directly toward Earth, has a speed of 12 km/s relative to the planet when the asteroid is 10 Earth radii from Earth’s center. Neglecting the effects of Earth’s atmosphere on the asteroid, find the asteroid’s speed v when it reaches Earth’s surface.arrow_forwardA planet moves in an elliptical orbit around a star. vp is the component of the planet's linear velocity that is perpendicular to r, the position vector of the planet. Consider two points - A and B - on the orbit. The distance (from the star to the planet) rA and rв are related as follows: TA = 0.3 TB .Neither of these two distances is the shortest or longest distance. (a) Vp,B is the magnitude of vp at point B and VpA is the magnitude of vp at point A. Calculate the ratio "p.B Vp.A (b) Calculate the ratio of the angular speeds of the planet at the two points WB A & B: WAarrow_forward
- In 1993 the spacecraft Galileo sent home an image (the figure) of asteroid 243 Ida and a tiny orbiting moon (now known as Dactyl), the first confirmed example of an asteroid-moon system. In the image, the moon, which is 1.5 km wide, is 100 km from the center of the asteroid, which is 55 km long. The shape of the moon's orbit is not well known; assume it is circular with a period of 27 h. (a) What is the mass of the asteroid? (b) The volume of the asteroid, measured from the Galileo images, is 14100 km³. What is the density (mass per unit volume) of the asteroid? (a) Number (b) Number A tiny moon (at right) orbits asteroid 243 Ida. (Courtesy NASA) Units Unitsarrow_forwardAn inventor wants to launch small satellites into orbit by launching them straight up from the surface of the earth, at very high speeds. a) With what speed should he launch the satellite if it is to have a speed of 500 m/s at a height of 400 km? Ignore air resistance. b) By what percentage would your answer be in error if you used a flat earth approximation? y2 400 km r, = R, + y2 vy= 500 tm/s After: Yi =0 km n = R Before: Re Eartharrow_forwardAn artificial satellite is moving in a circular orbit around the Earth with a speed equal to half the magnitude of escape velocity from the Earth. (a) Determine the height of the satellite above the earth's surface. (b) If the satellite is stopped suddenly in its orbit and allowed to fall freely onto the Earth, find the speed with which it hits the surface of the Earth.arrow_forward
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