Question

Volcano Puu Puai in Hawaii was formed in 1959 when a massive “lava fountain” erupted. The lava shot from the ground with an initial velocity of 350 feet per second.

a. For how long was the lava in the air until it returned to the ground?
b. What was the maximum height of the lava?
c. After how many seconds did the maximum height occur?

Answer 1

a)Tt = 21,41 s

b) y(max) = 1873 ft

c) t = 10,70 s

Explanation:

We assume that this is a case of vertical shooting then:

a) Vf = V₀ - g*t

Vf = 0 -g*t = -V₀

t = V₀ /g t = 350 ft/s / 32,7 ft/s²

t = 10,70 s time for lava to reach y maximum

a) Then Tt = 2*10,7 Tt = 21,41 s

Lava was in the air for Tt = 21,41 s

b) y = y₀ + v₀*t - (1/2 )*g*t²

for y = ymax we get:

y(max) = 0 + 350*10,70 - 0,5* 32,7* ( 10,70)²

y(max) = 3745 - 1872

y(max) = 1873 ft

c) t = 10,70 s