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Problem 8 Easy Difficulty

The space probe Deep Space 1 was launched on October 24, 1998. Its mass was 474 kg. The goal of the mission was to test a new kind of engine called an ion propulsion drive. This engine generated only a weak thrust, but it could do so over long periods of time with the consumption of only small amounts of fuel. The mission was spectacularly successful. At a thrust of 56 mN how many days were required for the probe to attain a velocity of 805 m/s (1800 mi/h), assuming that the probe started from rest and that the mass remained nearly constant?

Answer

79 days

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Video Transcript

these questions have to calculate how much time is taken from the probe to go from being equal zero to be equals 28 or five meters per second. So how can you do that? We begin by remembering that acceleration is defined as the variation in the velocity divided. By the time that such variation took toe a queer, then we can. So for Delta T to get at the time is close to the variation in the velocity divided by the acceleration. No, the variation in the velocity is close to 805 but we don't know what is the acceleration. Then we have to complete declaration. But how can we do that? Well near We have Booth, the Force and the Mass so we can use Newton's second of all for that mission. Newton's second law tells us that the net force is because to the mass times acceleration, the net force is close to 50 really turned to the ministry mutants, and these is equals 2 474 kinds of acceleration. Therefore, the acceleration is it goes to 56 thanks 10 to minus street divided by 474. Then we can plug in these results. You need equation to get that the interval of time required for the regulation toe. A core is equal to 805 divided by 56 times 10 to the minus street. Invited by 474. And these is equals true. 474 times. 805 divided by 56 Time. Stan, come on. The street is approximately 6.8 time, Stan for the six seconds and then we can convert this time from seconds days. How can you do that? Well, remember the following the vehicles to 6.8. I'm Stan to the six, divided by something. Now, remember, each day has going to four hours each hour, 60 minutes, and each minute, six seconds on down is Wilson is the single off time you may. And these is approximately 79. The