標題:
Derivatives 大high 手!
發問:
1. A balloon rises into the air from a point 250 meters away from an abserver. The angle between her line of sight and the ground increase at a rate of 0.04 rad per second. Find the rate at which the balloon is rising when the angle is 兀/3. 感恩不盡!!!!
最佳解答:
其他解答:
Derivatives 大high 手!
發問:
1. A balloon rises into the air from a point 250 meters away from an abserver. The angle between her line of sight and the ground increase at a rate of 0.04 rad per second. Find the rate at which the balloon is rising when the angle is 兀/3. 感恩不盡!!!!
最佳解答:
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Let θ be the angle of elevation and h be the height of the ballon. Then, h/250 = tan θ Differentiating both sides with respect to t, 1/250 dh/dt = sec2θ dθ/dt Since the angle of elevation is increasing at a rate of 0.04 radian per second, dθ/dt = 0.04. 1/250 dh/dt = sec2(π/3) 0.04 dh/dt = 250 * [1 / cos2(π/3)] * 0.04 = 10 * [1 / (1/2)2 = 40 m/s Hope it helps! ^^ 2006-12-07 06:08:04 補充： So the balloon is rising at a rate of 40 m per second.其他解答:
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