The acceleration due to gravity, g, is constant at sea level on the Earth's surface. However, the acceleration decreases as an object moves away from the Earth's surface due to the increase in distance from the center of the Earth. Derive an expression for the acceleration due to gravity at a distance h above the surface of the Earth, gh. Express the equation in terms of the radius R of the Earth, g, and h. 8h = Suppose a 70.00 kg hiker has ascended to a height of 1815 m above sea level in the process of climbing Mt. Washington. By what percent has the hiker's weight changed from its value at sea level as a result of climbing to this elevation? Use g = 9.807 m/s² and R = 6.371 × 106 m. Enter your answer as a positive value. weight change = %

An astronaut is rotated in a horizontal centrifuge at a radius of 5.6 m. How many revolutions per minute are required to produce if the centripetal acceleration has a magnitude of 5.3g? ( g is the gravitational acceleration, g=9.80 m/s2. Your result must include one digit after the decimal point. Maximum of 5% of error is accepted in your answer. Take  π=3.14)

Problem 2: Given vectors: A = 3 i+j- k, B = - i+ 2j+ 5 k, C = 2 j - 3 k. Find: 1. C. (A + B) 2. Cx (A - B)