一道数学题目,英文的A missile is fired vertically from a point that is 5 mi from a tracking station and at the the same elevation. For the first 20 sec. of flight , its angle of elevation changes at a constant rate of 2° per socond. Find the

Question

一道数学题目,英文的
A missile is fired vertically from a point that is 5 mi from a tracking station and at the the same elevation. For the first 20 sec. of flight , its angle of elevation changes at a constant rate of 2° per socond. Find the velocity of the missile when the angle of elevation is 30°.
要解一下,过程能越详细越好..

Answer 1

先翻译一遍问题：一枚导弹竖直发射,在五英里外有一个与发射点水平的观察站.在前20秒,观察站观测的仰角以每秒钟2°的速率提升.求仰角为30°是导弹对应的速率.
如图所示 设地面距离为 s=5  竖直高度为 h 仰角为 a 
此题的关键就是求出h-a函数,然后利用导数求出瞬时速率.
根据几个式子推导：
1   tan a =(h/s) 推出 h = tan a * s //三角函数定义
2   可以推出  h=tan a *s = 5tan a
所以 h` = 5(1+tan²a) //求导公式 ,
将a=30带入 的瞬时速率 为 20/3