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A 2300 kg rocket shuts off its engine 494km above earth's surface. Its velocity at burnout is 3000 m/s directly upward. Ignoring air resistance, what maximum height will the rocket reach?

Answer 1

Nolan Aldridge

#530035color(white)im#

#2aS=v^2-u^2#

#=>S=(v^2-u^2)/(2a)#

Enter the values:

#S=(0^2-3000^2)/(2xx8.49)#

#S=-9000000/16.98#

#S=530035color(white)im#

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Answer 2

Evan Ashley

The formula to calculate the maximum height ( h ) is [ h = \frac{v^2}{2g} ] where ( g ) is the acceleration due to gravity (9.8 m/s^2) and ( v ) is the rocket's final velocity at burnout (3000 m/s). Using the equations of motion and conservation of energy, this yields a result of [ h = \frac{3000^2}{2 \times 9.8} = \frac{9000000}{19.6} = 459183.67 , \text{m} ], the maximum height the rocket will reach.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.