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A projectile is launched horizontally with an initial speed of sqrt(2gh) from the top of a tower of height h. At what horizontal distance x from the base of the tower does it strike the ground?

1. 2h
2. h/2
3. h
4. 3h/2

Correct answer: 2h

Solution

The projectile falls a height h under gravity with no initial vertical velocity. Time of flight: h = (1/2)g*t², so t = sqrt(2h/g). Horizontal distance: x = v0*t = sqrt(2gh)*sqrt(2h/g) = sqrt(4h²) = 2h.

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