Question

A firework is fired from the ground straight up on a planet with an acceleration due to gravity of 10.56 m/s/s. The firework will not explode until the moment where it would have started to move back down again. The initial speed of the firework is 90.1 m/s. Use this information to find the height at which the firework explodes and the time it will be traveling upward.

Answer 1

h = 384.4 m

t = 8.5 s

Step-by-step explanation:

The firework will explode at the highest point. Because it would start to move downward at the highest point. Using 3rd equation of motion:

2ah = Vf² - Vi²

where,

a = acceleration due to gravity at that planet = -10.56 m/s²

h = maximum height = ?

Vf = Final velocity = 0 m/s (since, firework stops at highest point)

Vi = Initial Velocity = 90.1 m/s

Therefore,

2(-10.56 m/s²)(h) = (0 m/s)² - (90.1 m/s)²

h = 384.4 m

Now, we use 1st equation of motion:

Vf = Vi + at

0 m/s = 90.1 m/s + (-10.56 m/s²)(t)

t = 8.5 s