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A model rocket blasts off from the ground, rising straight upward with a constant acceleration that has a magnitude of 90.9 m/s2 for 1.82 seconds, at which point its fuel abruptly runs out. Air resistance has no effect on its flight. What maximum altitude (above the ground) will the rocket reach?

Respuesta :

Answer:

1547 m

Explanation:

a = 90.9 m/s2

t = 1.82 s

Vi = 0 m/s

Vf = Vi + at

= 0 + 90.9*1.82

= 165.44 m/s

Distance travelled at 1.82s, Si = Vi*t + 1/2 * a*t^2

= 0 + 1/2 * 90.9*(1.82^2)

= 150.55 m

At the point the fuel is exhausted, the rocket acts under gravity, Vf = Vi while Vf = 0 m/s (at rest). Its kintic energy = potential energy.

Therefore, a = -9.8 m/s

Vi = 165.44 m/s

Vf = 0

Using, Vf^2 = Vi^2 + 2a*Sf

Calculating the distance, Sf at potential energy,

= (0 - 165.44^2)/-9.8*2

= 1396.45 m

Maximum altitude, Stotal = Si + Sf

= 150.55 + 1396.45

= 1547 m

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