The Columbia Accident. On January 16, 2003, 81.7 seconds into the ascent, a piece of foam, weighing about 1.7 pounds, and being roughly the size, shape and weight of a large loaf of bread, separated from the bipod ramp of the space shuttle Columbia's external fuel tank and impacted the leading edge of the shuttle's left wing. At that time the shuttle was traveling at approximately 1,568 mph (Mach 2.46) and was at an altitude of 66,000 feet. Based on film evidence, the foam traveled the 58-foot distance from the ramp to the wing in 0.16 seconds. Assuming a constant acceleration relative to the body of the space shuttle of feet per second squared, the foam hit the wing at a speed of feet per second, or miles per hour. Unbeknownst to the astronauts and observers on earth, it struck the wing hard enough to cause the destruction of the Columbia two weeks later during re-entry on February 1, 2003.

Note: A much more involved calculation estimated the speed of the impact to be about 530 mph.

Remember that ww expects your answer to be within one tenth of one percent of what it considers the true answer. Calculate your answers based on the given data and assumptions to at least four digits.
Hint: Figure everything relative to the moving space shuttle, i.e., the origin is traveling with the shuttle. Acceleration is the derivative of velocity, and velocity is the derivative of displacement. In this case, the acceleration is constant (by assumption), and the initial velocity and displacement are 0. After 0.16 seconds the displacement is 58 feet. There are 3,600 seconds in an hour, and 5280 feet in a mile. As in many real problems, the problem statement contains extraneous information. You have to decide what parts of the information are pertinent.