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A toy rocket, launched from the ground, rises vertically with an acceleration of [tex]16 \, \text{m/s}^2[/tex] for [tex]2.7 \, \text{s}[/tex] until its motor stops. Disregarding any air resistance, what maximum height above the ground will the rocket achieve? The acceleration of gravity is [tex]9.8 \, \text{m/s}^2[/tex].

Answer in units of km.

Answer :

Final answer:

The maximum height reached by the toy rocket is approximately 7.0 km.

Explanation:

To calculate the maximum height reached by the toy rocket, we can use the kinematic equation: Δy = v₀t + 0.5at². Given that the initial velocity (v₀) is 0 m/s, the acceleration (a) is 16 m/s² for 2.7 s, and the acceleration due to gravity (g) is -9.8 m/s², we can substitute these values into the equation. By solving for Δy, we find that the maximum height the rocket will achieve is approximately 7.0 km.

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