Question

The acceleration due to gravity g near the surface of the Earth can be measured by projecting an object vertically upward and measuring the time that it takes to pass two given points in both directions. See the diagram below. Notice that the horizontal axis is time not position the path of the object is purely along a straight, vertical line. Show that if the time the body takes to pass a horizontal line A in both directions is T_A, and the time to go by a second line B in both directions is T_B, then, assuming that the acceleration is constant, its magnitude is g = 8h/T^2_A - T^2_B where h is the height of line B above line A. Explicitly verify that this expression has the appropriate dimensions.

Note: Show this using kinematic equations, please.

Answer 1

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