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:

aa.jpg

 

此文章來自奇摩知識+如有不便請留言告知

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:
arrow
arrow
    文章標籤
    自由行 文章 杭州 美心 上海
    全站熱搜

    oob73zj92b 發表在 痞客邦 留言(0) 人氣()

    E-mail轉寄