Question

Eyjafjallajökull is a Volcano in Ice land. During a recent eruption, the volcano, spewed out copious amounts of ash. One small was ejected from the volcano with an initial velocity of 368ft/sec. The height H, in feet, of our ash projectile is given by the equation H= -16t +368t

1. When does the ash projectile reach its maximum height?
2. What is its maximum height?
3. When does the ash projectile return to the ground?

Answer 1

1. The maximum height is at H` ( t ) = 0
H` ( t ) = ( -16 t² + 368 t )` = - 32 t + 368
- 35 t + 368 = 0
35 t = 368
t = 368 : 32
t = 11.5 sec.
2. H max = - 16 · 11.5² + 368 · 11.5 = - 2,116 + 4.232
H max = 2,116 ft
3. It returns to the ground after:
t = 2 · 11.5 = 23 seconds.