# 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?

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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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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.

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.

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.

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