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.

Question

Alessandro Ross

Physics

26 August, 22:28

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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Answers (1)

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Alejandro Christensen · Answer 1

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