0
You visited us 0 times! Enjoying our articles? Unlock Full Access!
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 $${ \theta }_{ 0 }=35$$ to the horizontal, from the vent at $$A$$ in order to fall at the foot of the volcano at $$B$$, at vertical distance $$h=3.30 km$$ and horizontal distance $$d=9.40 km$$? Ignore, for the moment, the effects of air on the bombs travel. (b) What would be the time of flight? (c) Would the effect of the air increase or decrease your answer in (a)?

Solution
Verified by Toppr

(a) For projectile motion $$v_o$$ is given by formula$${ v }_{ 0 }=\dfrac { x }{ cos{ \theta }_{ 0 } } \sqrt { \dfrac { g }{ 2(xtan{ \theta }_{ 0 }-y) } }$$putting $$x = 9400 m$$, $$y = –3300 m$$, and $${ \theta }_{ 0 } = 35°$$.$${ v }_{ 0 }=\dfrac { 9400 }{ \cos35^o } \sqrt { \dfrac { g }{ 2(x\tan35^o-3300) } }$$$${ v }_{ 0 }= 255.5 ≈ 2.6 × { 10 }^{ 2 }m/s$$ (b) For projectile motion $$t$$ is given by formula$$t=\dfrac { x }{ { v }_{ 0 }{ cos\theta }_{ 0 } }$$$$t=\dfrac { 9400m }{ (255.5m/s)cos{ 35 }^{ o } } =45s.$$(c) We expect the air to provide resistance but no appreciable lift to the rock, so we would need a greater launching speed to reach the same target.

4
Similar Questions
Q1
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 $${ \theta }_{ 0 }=35$$ to the horizontal, from the vent at $$A$$ in order to fall at the foot of the volcano at $$B$$, at vertical distance $$h=3.30 km$$ and horizontal distance $$d=9.40 km$$? Ignore, for the moment, the effects of air on the bombs travel. (b) What would be the time of flight? (c) Would the effect of the air increase or decrease your answer in (a)?

View Solution
Q2
Figure shows three paths for a football kicked from ground level. Ignoring the effects of air, rank the paths according to (a) time of flight, (b) initial vertical velocity component, (c) initial horizontal velocity component, and (d) initial speed, greatest first.

View Solution
Q3
An airplane flying horizontally at a constant speed of $$350 \,km/h$$ over level ground releases a bundle of food supplies. Ignore the effect of the air on the bundle. What are the bundles initial (a) vertical and (b) horizontal components of velocity? (c) What is its horizontal component of velocity just before hitting the ground? (d) If the airplanes speed were, instead, $$450 \,km/h$$, would the time of fall be longer, shorter, or the same?
View Solution
Q4

An airplane flying horizontally at a constant speed of 350 km/h over level ground releases a bundle of food supplies. Ignore the effect of the air on the bundle.What are the bundle’s initial (a) vertical and (b) horizontal components of velocity? (c) What is its horizontal component of velocity just before hitting the ground? (d) If the airplane’s speed were, instead, 450 km/h, would the time of fall be longer,shorter,or the same?

View Solution
Q5
An airplane moving horizontally at a speed of 100 m/s and at a height of 103 in is to drop a bomb on a target. At what horizontal distance from the target should the bomb be released:
View Solution