Answer:
i) -28 ft/s
ii) -21.6 ft/s
iii) -20.8 ft/s
iv) -20.16 ft/s
b) -20 ft/s
Step-by-step explanation:
if v represents vertical velocity then if the height y is
y = 44*t − 16*t²
and the instant velocity v is the derivative with respect to the time
v= dy/dt = 44*(1) - 16*(2*t) = 44- 32*t
while the average velocity is va= (y-y₀)/(t-t₀)
where t₀ = 2 and y₀=y(t₀) = 44*2 − 16*2² = 24
then
va= (y-y₀)/(t-t₀) = (44*t − 16*t² - 24)/(t-2)
for
i) t= 0.5s + 2 s= 2.5 s
va = (44* 2.5 − 16* 2.5 ² - 24)/( 2.5 -2) = -28 ft/s
ii) t= 0.1s + 2 s= 2.1 s
va = (44* 2.1 − 16* 2.1 ² - 24)/( 2.1 -2) = -21.6 ft/s
iii) t= 0.05 s + 2 s= 2.05 s
va = (44* 2.05 − 16* 2.05 ² - 24)/( 2.05 -2) = -20.8 ft/s
iv) t= 0.01s + 2 s= 2.01 s
va = (44* 2.01 − 16* 2.01 ² - 24)/( 2.01 -2) = -20.16 ft/s
b) the instantaneous velocity when t=2
v (t=2) = 44- 32*(2) = -20 ft/s
