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. At what initial speed would a bomb have to be ejected, at angle theta_0 = 31 degree to the horizontal, from the vent at A in order to fall at the foot of the volcano at B, at vertical distance h = 3.100 km and horizontal distance d = 9.50 km? Ignore, for the moment, the effects of air on the bomb's travel. What would be the time of flight?

Explanation / Answer

let the spped be u km/hr and time is t hr

for horizontal direction, d = u*cos *t
9.5= u*cos 31 *t
9.5= 0.857*u*t
u = 11.09/t

for vertical distance,
-h = u*sin *t + 0.5*a*t^2
-3.10 = u*t*sin 31 - 0.5*9.8*t^2
-3.10 = (11.09/t)*t*sin 31 - 0.5*9.8*t^2
-3.10 = 5.712 - 4.9*t^2
t = 1.34 hr

u = 11.09/t
= 11.09/1.34
=8.27 km/hr

Answer:
a)
8.27 km/hr
b)
1.34 hr

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