Angle Finder
Help calculation?
On-air balloon is rising upward from a field, and is followed by a rangefinder 500 feet breakpoint lift. the balloon rises at a rate of 15 feet per second. A) How fast is the direct distance between the rangefinder and the ball changes by 5 seconds B) How fast is the angle of elevation change when the balloon is 500 feet high, it gave us a diagram a right to trianle hypotenuse labeled D and the side labeled h and 500 equaling the bottom
Based on your data Let D = Hypotenuse of the triangle (which is the distance the ball at the range finder at any time "t") h = height of the ball on the ground at any time "t" b = distance from the station continued recovery point off the ball. Your original equation is d ^ 2 = H ^ 2 + b ^ 2 Differentiate above, 2D (dd / Dt) = 2h (dh / dt) + 2b (dB / dt) Since db / dt = 0 (the distance between the point of taking off and the monitoring station does not change because it is always equal to 500 ft.) above simply becomes 2D (dd / dt) = 2h (dh / dt) + 0 simplify, d (dd / dt) = h (dh / dt) Resolution to (dd / dt). (Dd / Dt) = (h / d) (dh / dt) – call this equation NOTE that dh / dt = 15 m / sec (given) h = 15 * 5 = 75 and = sqrt (75 ^ 2 + 500 ^ 2) = sqrt (5625 + 250 000) d = sqrt (255 625) d = 506 ft substituting the values into the equation, (dd / dt) = (75/506) * 15 = 2.22 m / sec. **************************************** Let A = angle of elevation of the hot air balloon from the geometry of the figure, tan A = h/500 Differentiating the above, d (tan A) / dt = (dh / dt) / 500 I trust that you can do the math required procedure from here.
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