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Math Help - Motion problems #2

  1. #1
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    Motion problems #2

    Can someone please show me the steps needed to achieve the answers to this question?

    Leonard need to get to Penny's house from his apartment- her house is just across a 4km wide river and is 3km upstream from Leonard's apartment with a current of 1km/h toward the east. Leonard can do one of two things: 1) he can swim on a path straight to Penny's house or 2) he can swim straight across the river and run the rest of the way on land. His swimming speed is 4km/h and his running speed is 6km/h. Which method will get Leonard to Penny's the fastest?

    any help is much appreciated. =)
    Last edited by mr fantastic; April 9th 2010 at 07:08 PM. Reason: Moved a question to this subforum, edited new post title
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  2. #2
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    Quote Originally Posted by Hellooo View Post
    Can someone please show me the steps needed to achieve the answers to this question?

    Leonard need to get to Penny's house from his apartment- her house is just across a 4km wide river and is 3km upstream from Leonard's apartment with a current of 1km/h toward the east. Leonard can do one of two things: 1) he can swim on a path straight to Penny's house or 2) he can swim straight across the river and run the rest of the way on land. His swimming speed is 4km/h and his running speed is 6km/h. Which method will get Leonard to Penny's the fastest?

    any help is much appreciated. =)
    What have you tried? Where are you stuck?
    Last edited by mr fantastic; April 9th 2010 at 07:03 PM.
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  3. #3
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    I found the time it requires(1.2h, not totally sure if i'm correct) to travel directly across the river, but i'm not sure how to get the 2nd part.

    I used the cosine law to find the velocity of Leonard swimming against the current( I got about 4.7km/h). After that i used the sine law to find the distance between Penny and Leonard which got 5.8km. I found the time by dividing the distance by velocity which appears to be 1.2h, which I'm not sure is correct.
    After that i found the time for 2nd method which turned out to be 1.7h which again I'm not sure if it's correct.
    Last edited by mr fantastic; April 9th 2010 at 07:18 PM. Reason: Merged posts
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  4. #4
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    I'm not quite sure how to explain how i did it, but i a scanned picture of what i did.

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