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A 1.7-kg firework is fired from the ground straight up on a planet with whose acceleration due to gravity is 4.8 m/s/s. You want the firework to explode when it is at a height of 165 m. You want the firework to be moving down at a speed of 10.0 m/s when it explodes. Use this information to find out how fast you should launch your firework and how much time you should have on your trigger.

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MathPhys

Answer:

41.0 m/s, 10.6 s

Explanation:

Given:

a = -4.8 m/s²

Δy = 165 m

v = -10.0 m/s

Find: v₀ and t

v² = v₀² + 2aΔy

(-10.0 m/s)² = v₀² + 2(-4.8 m/s²) (165 m)

v₀ = 41.0 m/s

Δy = vt − ½ at²

165 m = (-10.0 m/s) t − ½ (-4.8 m/s²) t²

165 = -10t + 2.4t²

0 = 2.4t² − 10t − 165

Solve with quadratic formula:

t = [ -(-10) ± √((-10)² − 4(2.4)(-165)) ] / 2(2.4)

t = (10 ± √1684) / 4.8

t = 10.6 s

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