Q2: When you throw a ball into the air, it usually falls back down. If you throw it a little harder, it will take longer to fall back down. You can throw it so hard that it never falls back down to Earth. This launch speed is called the escape velocity. When you are far from Earth, the potential energy of an object with mass m can no longer be written as U = mgh. Instead, we must use the equation U = -GMm r M is the mass of the planet you launch from. m is the mass of the object being launched. r is the distance from the center of the planet to the object being launched. G is a universal constant G = 6.674 x 10-¹¹ N. m²/kg² Notice that the potential energy is O when you are infinitely far away from the planet, and negative as you get closer. Using the above equation and what you know about kinetic energy and energy conservation, show that the expression 2GM for the escape velocity ve from a planet of radius Ris v (Hint: To just escape the planet, the object's R final speed must be 0 infinitely far from the planet.) and find the escape velocity of an object being launched from Earth. Earth has a radius of RE = 6.37 x 106 m and a mass of ME = 5.97 x 1024 kg

Q2: When you throw a ball into the air, it usually falls back down. If you throw it a little harder, it will take longer to fall back down. You can throw it so hard that it never falls back down to Earth. This launch speed is called the escape velocity. When you are far from Earth, the potential energy of an object with mass m can no longer be written as U = mgh. Instead, we must use the equation U = -GMm r M is the mass of the planet you launch from. m is the mass of the object being launched. r is the distance from the center of the planet to the object being launched. G is a universal constant G = 6.674 x 10-¹¹ N. m²/kg² Notice that the potential energy is O when you are infinitely far away from the planet, and negative as you get closer. Using the above equation and what you know about kinetic energy and energy conservation, show that the expression 2GM for the escape velocity ve from a planet of radius Ris v (Hint: To just escape the planet, the object's R final speed must be 0 infinitely far from the planet.) and find the escape velocity of an object being launched from Earth. Earth has a radius of RE = 6.37 x 106 m and a mass of ME = 5.97 x 1024 kg