Because of your knowledge of physics, you have been hired as a consultant for a new James Bond movie, "Oldfinger". In one scene, Bond jumps horizontally off the top of a cliff to escape a villain. To make the stunt more dramatic, the cliff has a horizontal ledge a distance h beneath the top of the cliff which extends a distance LL from the vertical face of the cliff. The stunt coordinator wants you to determine the minimum horizontal speed, in terms of L and h, with which Bond must jump so that he misses the ledge.
v = [√(g/2h)]L
Let v be the initial horizontal velocity, t be the time James Bond uses to jump over the ledge of length, L.
So, vt = L and t = L/v
Also, since James Bond has no initial horizontal velocity, he falls freely through the distance, h so we use the equation y - y' = ut - 1/2gt², where y = 0 (at the top of the cliff) and y' = -h, u = 0 (initial vertical velocity), g = acceleration due to gravity = 9.8 m/s² and t = the time it takes to jump off the cliff = L/v.
Substituting these values into the equation, we have
y' - y = ut - 1/2gt²
-h - 0 = 0 × t - 1/2g(L/v)²
-h = - 1/2gL²/v²
v² = gL²/2h
taking square root of both sides, we have
v = [√(g/2h)]L
So, James Bond's minimum horizontal speed is v = [√(g/2h)]L
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Physics, published 10.03.2023