A man starts walking north at 6 ft/s from a point P.Five minutes later,a woman starts walking south

题目

A man starts walking north at 6 ft/s from a point P.Five minutes later,a woman starts walking south at 4 ft/s from a point 470 ft due east of P.At what rate ( in ft/s ) are the people moving apart 15 min after the woman starts walking?Please round your answer to the nearest hundredth

答案

题目要求女人出发15min中两人相距距离增加的速率,只要求出两人距离关于时间的函数,然后求微分就可以求得.而两人距离y^2=470^2+(6*5*60+6t+4t)^2即y=根号下(470^2+(1800+10t)^2),然后求微分,再把t=15*60=900代入,得到...