Question

一汽車行駛時(shí)遇到緊急情況，駕駛員迅速正確地使用制動(dòng)器在最短距離內(nèi)將車停住，稱為緊急制動(dòng)，設(shè)此過程中使汽車減速的阻力與汽車對(duì)地面的壓力成正比，其比例系數(shù)只與路面有關(guān)。已知該車以72km/h的速度在平直公路上行駛，緊急制動(dòng)距離為25m；若在相同的路面上，該車以相同的速率在坡度（斜坡的豎直高度和水平距離之比稱為坡度）為1：10的斜坡上向下運(yùn)動(dòng)，則緊急制動(dòng)距離將變?yōu)槎嗌�？�?i>g=10m/s²，結(jié)果保留兩位有效數(shù)字）

Answer 1

 S₂=29m

以汽車初速度方向?yàn)檎�方向，設(shè)質(zhì)量為m的汽車受到的阻力與其對(duì)路面壓力之間的比例系數(shù)為μ，在平直公路上緊急制動(dòng)的加速度為a₁。
根據(jù)牛頓第二定律 －μmg=ma₁  ·················································································· ①
根據(jù)勻減變速直線運(yùn)動(dòng)規(guī)律 a₁＝ ·········································································· ②
聯(lián)立解得 μ＝＝0.8
設(shè)汽車沿坡角為θ的斜坡向下運(yùn)動(dòng)時(shí)，緊急制動(dòng)的加速度為a₂，制動(dòng)距離為S₂。
根據(jù)牛頓第二定律 mgsinθ－μmgcosθ＝ma₂······································································ ③
根據(jù)勻變速直線運(yùn)動(dòng)規(guī)律 S₂＝··············································································· ④
由題意知tanθ=0.1，則  sinθ＝≈0.1        cosθ＝≈1
聯(lián)立解得 S₂="29m" ··································································································· ⑤
說明：若用其他方法求解，參照參考答案給分。
；28.57m