a bottle rocket takes off with an acceleration of 34.5m/s^2. it fires until it reaches a height of 200m, then shuts off, and gravity takes over. what maximum height does it reach? (unit = m)

904 m

Explanation:

First, find the velocity reached when the rocket shuts off.

Given:

Δy = 200 m

v₀ = 0 m/s

a = 34.5 m/s²

Find: v

v² = v₀² + 2aΔy

v² = (0 m/s) ² + 2 (34.5 m/s²) (200 m)

v ≈ 117.5 m/s

Now find the height reached during free fall.

GIven:

y₀ = 200 m

v₀ = 117.5 m/s

v = 0 m/s

a = - 9.8 m/s²

Find: y

v² = v₀² + 2aΔy

(0 m/s) ² = (117.5 m/s) ² + 2 (-9.8 m/s²) (y - 200 m)

y ≈ 904 m