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

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let velocity be u

=30 degrees

h = 1.6 km = 1600 m

d = 2.4 km = 2400 m

horizontal initial velocity,ux = ucos

vertical initial velocity,uy = usin

let final velocity be v and its component be vx and vy

let time in flight be t

for landing at base

ux*t = d = 2400m ------------------------(1)

-h = uy*t - 0.5gt^2 => uy*t + h - 0.5gt^2 = 0 ----------------------(2)

from (1) ucos*t = 2400

u = 2400/tcos------------(3)

from (2)

usin*t + 1600-4.9t^2 = 0 -----------------(4)

from (3) and (4)

2400tan + 1600- 4.9t^2=0

=30 degrees

hence solvin gives,t = 24.68 s Ans(b)

a)from (1)

u = 2400/tcos = 112.29 m/s Ans(a)

change in KE = 0.5m(v^2-u^2)

change in PE = mgh

since change in PE = change in KE

0.5m(v^2-u^2)=mgh

putting values, cancelling m and solving for v gives

v = 209.69 m/s Ans(c)

acceleration is always same and equal to g

a = 9.8 m/s^2 Ans(d)

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