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Math Help - calculate the rate of change of this hot air balloon

  1. #1
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    Question calculate the rate of change of this hot air balloon

    A hot air balloon rises straight up from a level field and is detected by a range finder 200 m from the lift off point. At that point, the angle of elevation of the balloon is 60 degrees, and the angle is increasing at the rate of 0.1 rad/min. Find the rate at which the balloon is rising when the angle of elevation of the balloon from the range finder is 45 degrees.

    Could someone please show me the full steps

    Thanks in advance
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  2. #2
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    Quote Originally Posted by differentiate View Post
    a hot air balloon rises straight up from a level field and is detected by a range finder 200 m from the lift off point. At that point, the angle of elevation of the balloon is 60 degrees, and the angle is increasing at the rate of 0.1 rad/min. Find the rate at which the balloon is rising when the angle of elevation of the balloon from the range finder is 45 degrees.

    Could someone please show me the full steps

    thanks in advance
    Code:
    |.
    |   .
    |      .
    |         .
    |            .
    |               .
    |h                 .
    |                     .
    |                        .
    |                       
    
    
    
    
    \theta   .
    |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 
                200
    \tan{\theta} = \frac{h}{200}

    \sec^2{\theta} \cdot \frac{d\theta}{dt} = \frac{1}{200} \cdot \frac{dh}{dt}

    45 degrees is pi/4 rad

    60 degrees is pi/3 rad

    When the angle is 45 degrees:

    200 \sec^2{\left(\frac{\pi}{4}\right)} \frac{d\theta}{dt}= \frac{dh}{dt}

    400\frac{d\theta}{dt}= \frac{dh}{dt}

    Now use the remaining information for when the angle is 60 degrees to finish the problem with simultaneous equations.

    Hope that was helpful

    Mathemagister
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  3. #3
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    sorry. but I still don't get it.
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  4. #4
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    I put in theta = pi/3, with the remaining info and I got
    dh/dt = 80 metres/min when theta = pi/3 and d(theta)/dt = 0.1

    but how do i solve simultaneously with this info and the info,
    400 (d(theta)/dt = dh/dt) ?
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