Ifaballisthrownintheairwithavelocity42ft/s,itsheightinfeettsecondslaterisgivenbyy=42t−16t2.(a)Findtheaveragevelocityforthetimeperiodbeginningwhent=2andlasting(i)0.5second.30.00ft/s(ii)0.1second.ft/s

Question

If a ball is thrown in the air with a velocity 42 ft/s,its height in feet t seconds later is given by y = 42t − 16t2.
(a) Find the average velocity for the time period beginning when t = 2 and lasting
(i) 0.5 second.
30.00
ft/s
(ii) 0.1 second.
ft/s
23.60
(iii) 0.05 second.
ft/s
22.80
(iv) 0.01 second.
22.16
ft/s
(b) Estimate the instantaneous velocity when t = 2.
ft/s
22.00

Answer 1

y=42t-16t^2
vh=42-32t;
vh0=42;可以看出球是垂直上抛,水平方向速度是0
tlast=21/8=2.625s
vmiddle=0;
tmiddle=21/16=1.3225s ;2>1.3225;是下落途中
y2=84-64=20f
总距离 S=y2-0=20f
总时间 t=2.625-2=0.625;
v=s/t=32(f/s)