船在400米寬的河中橫渡,河水流速是2m/s,船在靜水中的航速是4m/s,要使船到達(dá)對(duì)岸的時(shí)間最短,船頭應(yīng)指向______,最短時(shí)間是______,要使船航程最短,船頭應(yīng)指向______最短航程______.
當(dāng)船頭的指向與河岸垂直時(shí),渡河時(shí)間最短,最短時(shí)間t=
=s=100s.
當(dāng)合速度方向與河岸垂直時(shí),渡河位移最短,設(shè)船頭的指向與河岸的夾角為θ,有cosθ=
=,則θ=60°.即船頭指向與上游成60度角.
最短航程為400m.
故答案為:垂直正對(duì)岸,100s,與上游成60度角,400m.