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. Figure 4-51 shows a cross section of Mt. Fuji, in Japan. (a) At what initial speed would a bomb have to be ejected, at angle ?0 = 41° to the horizontal, from the vent at A in order to fall at the foot of the volcano at B, at vertical distance h = 3.40 km and horizontal distance d = 8.90 km? Ignore, for the moment, the effects of air on the bomb's travel. (b) What would be the time of flight?

Explanation / Answer

yo=ht=3400 m from top of volcano to ground--->theta=41 degrees---> distance=8900 m--->ay=9.8 m/s^2--->ax=0 vo=sqrt((g*x^2)/(2*cos(theta)^2*(x*tan(theta)-yo)))=396.4 m/s vox=vo*cos(41 degrees)=299.2 m/s--->vo*sin(41 degrees)=260.1 m/s max ht=3400+voy^2/(2*g)=6850.62 m--->max ht t=voy/g=26.54 s (-voy+sqrt(voy^2+4*1/2*g*yo))/(-2*4.9)=-10.854 s--->26.54*2+10.854=63.93 s a) vo=396.4 m/s b) 63.93 s total flight time

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