小偷逃跑的速度是360m/min,警察追捕的速度是27km/h,小偷在警察前90m处,如果小偷和警察都做匀速直线运动,问警察能不能在500m的路程内追上小偷?
解法一:小偷逃跑的速度V ′ =360m/min=6m/s,警察追捕的速度V=27km/h=7.5m/s; 警察跑500m的时间为:t=
在这段时间内小偷跑的距离为:S ′ =V ′ t=6m/s×66.7s=400.2m, S ′ +90m=400.2m+90m=490.2m<500m, 答:警察能在500m的路程上追上小偷. 解法二;设警察经时间t追上小偷, 则有:Vt=V ′ t+90m, 即:7.5m/s×t=6m/s×t+90m, 解得:t=60s, 60s内警察前进的距离为:s 1 =Vt=7.5m/s×60s=450m<500m, 答:警察经500m肯定能追上小偷. |