1>Suppose that a plane is at location f(0) = 10 miles with velocity of f’(0) = 10 miles/min, acceleration f’’(0) = 2 miles/min2 and f’’’(0) = -1 miles/min3. Predict the location of the plane at time t = 2.
2>The weight (force due to gravity) of an object of mass m and altitude x miles above the surface of the earth is w(x) = (mgR^2)/(R+x)^2, where R is the radius of the earth and g is the acceleration due to gravity. Show that w(x) is approximately mg(1-2x/R). Estimate how large x would need to reduce the weight by 10%.