During volcanic eruptions, chunks of solid rock can be blasted out of the volcan

Question

During volcanic eruptions, chunks of solid rock can be blasted out of the volcano; these projectiles are called volcanic bombs. The figure shows a cross section of Mt. Fuji, in Japan, (a) At what initial speed would a bomb have to be ejected, at angle theta_0 = 34 degree to the horizontal, from the vent at A in order to fall at the foot of the volcano at 8, at vertical distance h = 3.70 km and horizontal distance d = 10.7 km? Ignore, for the moment, the effects of air on the bomb's travel, (b) What would be the time of flight?

Explanation / Answer

horizontal distance = ucos34*t+1/2axt^2

ax = 0

x = ucos34*t

u = x/tcos34

verticle distance = usin34*t-1/2gt^2

h = xtan34-1/gt^2

1/2gt^2 = xtan34-h =10700tan34-3700

t = 26.79 sec

initial spped u = x/tcos34 = 10700/26.79cos34 = 481.2 m/sec

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