average velocity

Question

I keep getting the wrong answer for this, and cant figure out where my mistake is. 

A ball is thrown into the air by a baby alien on a planet in the system of Alpha Centauri with a velocity of 41 ft/s. Its height in feet after t seconds is given by  y=41t-27t^2.

A. Find the average velocity for the time period beginning when t=3 and lasting

.01 sec

.005 sec

etc.

 

my formula says that average velocity = h(t₂) - h(t1)/t₂-t₁

my interval would be [3,.01 ] where t-sub-one its 3, and t-sub-2 its .01

i do the math and keep getting 40.27 or -40.27

the correct answer its supposed to be -121.27

i've done the math on my graphing calc and by hand i just cant come up with -121.27

 

f(.01)-f(3)

f(.01) = 41(.01) - 27(.01)^2 = 0.4073

f(3) = 41(3) - 27(3)^2=-120

0.4073 - (-120) = 120.4073 

.01 - 3 = -2.99

120.4079 / -2.99 = -40.27

 

simple math, yet im wrong somewhere.

 

 

Answer 1

I will help you with the first one:

 

h(t₂) = 41(3.01) - 27(3.01²) = -121.2127

h(t₁) = 41(3) - 27(3²) = -120

t₂ - t₁ = 3.01 - 3.00 = 0.01

 

[h(t₂) - h(t₁)] / (t₂ - t₁) = (-121.2127 + 120) / (0.01) = -121.27

 

The answer you were given is correct.  You should be able to work the rest of them now.

Answer 2

Rick you are doing the right math but making a minor mistake with your t value. It says start at t = 3. So your time periods are actually

t_{1 =} 3 s

t₂ = 3+0.01 s = 3.01s

 

This should give you the right answer.