设时刻t时,气球的高度是h,则tanα＝h/200.当h＝200时,α＝π/4.
tanα＝h/200两边对t求导得
(secα)^2×dα/dt＝1/200×dh/dt
代入α＝π/4,dh/dt＝50,得dα/dt＝5/40＝0.125(弧度/分钟)