In the movie Volcano, solid chunks of rock, called lava bombs were ejected from

Question

In the movie Volcano, solid chunks of rock, called lava bombs were ejected from the growing volcano. Consider a volcano, shown below, with a lava bomb being ejected. (a) What would the magnitude of the initial velocity at the top of the volcano, have to be in order for a lava bomb to land at the base of the volcano? (b) What would be the time of flight of this projectile from the top of the volcano to its base? (c) What is the final velocity of the lava bomb just before it hits the ground at the base? (d) What is the acceleration of the lava bomb just before it hits the ground at the base?

Explanation / Answer

(a) What would the magnitude of the initial velocity at the top of the volcano, have to be in order for a lava bomb to land at the base of the volcano?

vx = x/t = 2.4e3/t

t = 2.4e3/vx

y = -0.5 g t^2 + vy t

==> -1600 = -0.5*9.8*(2.4e3/vx)^2 + vy * (2.4e3/vx)

==> -1600 = -28224000/(vx)^2 + tan(30) * (2.4e3)

==> -1600 = -28224000/(vx)^2 + 0.57735 * (2.4e3)

==> 2985.64 = 28224000/(vx)^2

==> vx = 97.228 m/s

==> vy = tan30 * vx = 0.57735 * 97.228 = 56.135 m/s

==> v = (97.228*97.228 + 56.135*56.135) = 112.27 112 m/s

(b) What would be the time of flight of this projectile from the top of the volcano to its base?

t = 2.4e3/vx = 2.4e3/97.228 = 24.684 24.7 s

(c) What is the final velocity of the lava bomb just before it hits the ground at the base?

vy = -gt + 56.135 = -9.8 * 24.684 + 56.135 = -185.77 m/s

==> v = (97.228*97.228 + 185.77*185.77) = 210 m/s

(d) What is the acceleration of the lava bomb just before it hits the ground at the base?

a = -g = -9.8 m/s2

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