二次方程 函数The following function gives the height,h metres,of a batted baseball as a function of the time,t seconds,since the ball was hit:h= -6(t-2.5)^2+ 38.5a) How many seconds after it was hit did the ball hit the ground ,to the nearest s
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二次方程 函数The following function gives the height,h metres,of a batted baseball as a function of the time,t seconds,since the ball was hit:h= -6(t-2.5)^2+ 38.5a) How many seconds after it was hit did the ball hit the ground ,to the nearest s
二次方程 函数
The following function gives the height,h metres,of a batted baseball as a function of the time,t seconds,since the ball was hit:
h= -6(t-2.5)^2+ 38.5
a) How many seconds after it was hit did the ball hit the ground ,to the nearest second?
请列出主要的演算步骤和式子.
二次方程 函数The following function gives the height,h metres,of a batted baseball as a function of the time,t seconds,since the ball was hit:h= -6(t-2.5)^2+ 38.5a) How many seconds after it was hit did the ball hit the ground ,to the nearest s
题目意思是当t=?时,t为整数,表达式-6(t-2.5)^2+ 38.5与0最接近.
令
-6(t-2.5)^2+ 38.5=0求出两根,分别为5.0331和-0.0331,在两根旁取三点,即0,5,6,分别代入原表达式中
当t=0,表达式为 1；
当t=5,表达式为 1；
当t=6,表达式为 -35；
又因为t>0且表达式为正数,
故当t=5时,离地面最近!
球高h为时间t的函数:h= -6(t-2.5)^2+ 38.5
那么球第1次落地时间显然h=0,求t
得t =2.5+(38.5/6)^(1/2),
而t =2.5-(38.5/6)^(1/2)<0,不适合
棒球着地，即高度h =0
则有0= -6(t-2.5)^2+ 38.5
(t-2.5)^2 = 77/12
t1 =sqrt(77/12) +2.5 近似5， sqrt为根号
t2=2.5-sqrt(77/12)<0
所以时间是t1,最接近的秒数是5s
当球落地时，h=0 即：-6(t-2.5)^2+ 38.5=0
-6(t^2-5t+6.25)+38.5=0
-6t^2+30t-37.5+38.5=0
6t^2-30t-1=0
解得：t=2.5±(√231)/6 t≈5或0
t=0不合题意
∴t=5