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Thread: Hot Air Balloon

  1. #1
    Super Member harpazo's Avatar
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    Hot Air Balloon

    A hot-air balloon, headed due east at an average speed of 15 mph and at a constant altitude of 100 feet, passes over an intersection. Find an expression for the distance d (measured in feet) from the balloon to the intersection t seconds later.

    I decided to draw an xy-plane. I let B = balloon located at a height of 100 feet described by the point on the y-axis (0, 100).
    I see the words AVERAGE SPEED, which quickly points me to the formula D = rt. I am thinking, however, the sought expression somehow involves the formula a^2 + b^2 = c^2. Seeking two hints.
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  2. #2
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    Re: Hot Air Balloon

    The balloon is moving horizontally, keeping a constant height. t hours after crossing the intersection, the horizontal distance from the intersection is 15t miles and the balloons vertical distance is 100 feet. The straight line distance from the intersection to the balloon is along the hypotenuse of a right triangle having the horizontal and vertical distances as legs. Yes, you need to use the Pythagorean theorem. Since the problem asks for the distance in feet in t seconds, you will need to convert 15 "miles per hour" to "feet per second".

    (There are 5280 feet in a mile and 3600 seconds in an hour.)
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    Super Member harpazo's Avatar
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    Re: Hot Air Balloon

    Quote Originally Posted by HallsofIvy View Post
    The balloon is moving horizontally, keeping a constant height. t hours after crossing the intersection, the horizontal distance from the intersection is 15t miles and the balloons vertical distance is 100 feet. The straight line distance from the intersection to the balloon is along the hypotenuse of a right triangle having the horizontal and vertical distances as legs. Yes, you need to use the Pythagorean theorem. Since the problem asks for the distance in feet in t seconds, you will need to convert 15 "miles per hour" to "feet per second".

    (There are 5280 feet in a mile and 3600 seconds in an hour.)
    The question is asking for an expression not an actual number or distance.
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  4. #4
    Junior Member Cervesa's Avatar
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    Re: Hot Air Balloon

    $d=\sqrt{(vt)^2+100^2}$, where $v$ = horizontal speed in ft/sec

    hint: 60 mph = 88 ft/sec (learned that from my drivers license test)
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  5. #5
    Super Member harpazo's Avatar
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    Re: Hot Air Balloon

    Thank you everyone.
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