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Math Help - trigonometry word problem

  1. #1
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    trigonometry word problem

    When an airplane leaves the runway, its angle of climb is 20 and its speed is 335 feet per second. How long will it take the plane to climb to an altitude of 10,000 feet? 16,000 feet?

    Here is how I am thinking about it:

    335 * 60 = 20100

    then 10,000 / 335 = 29.85 seconds.

    I am not sure if this is right but it is a guess. Could some one help me.
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  2. #2
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    You need to use the vertical component of the plane's velocity, which is 335 \sin 20 feet per second, to calculate the time taken to reach a certain altitude.
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  3. #3
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    vertical rate of climb is 335\sin(20) ft/sec

    now calculate time to climb ... t = \frac{altitude}{rate \,\, of \,\, climb}
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  4. #4
    A riddle wrapped in an enigma
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    Quote Originally Posted by robasc View Post
    When an airplane leaves the runway, its angle of climb is 20 and its speed is 335 feet per second. How long will it take the plane to climb to an altitude of 10,000 feet? 16,000 feet?

    Here is how I am thinking about it:

    335 * 60 = 20100

    then 10,000 / 335 = 29.85 seconds.

    I am not sure if this is right but it is a guess. Could some one help me.
    I looked at it this way.

    \sin20=\frac{h}{335} should yield the height in feet after 1 second.

    That's 335 \sin 20 ft. in 1 sec.

    Now, for 10000 feet, that'd be \frac{10000}{335 \sin 20} \approx 886 \ \ sec. \ \ or \ \ 14.8 \ \ min.

    Edit: Too slow on the post today!
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