Question: A spacecraft in deep space is programmed to increase its speed by a desired amount v by burning its engine for a specified time duration

A spacecraft in deep space is programmed to increase its speed by a desired amount Δv by burning its engine for a specified time duration t. Twenty-five percent of the way through the burn, the engine suddenly malfunctions and thereafter produces only half of its normal thrust. What percent n of Δv is achieved if the rocket motor is fi red for the planned time t? How much extra time t′ would the rocket need to operate in order to compensate for the failure?

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