Avg Velocities answer is wrong

Question

A ball is thrown into the air by a baby alien on a planet in the system of Alpha Centauri with a velocity of 36 ft/s. Its height in feet after t seconds is given by y=36t−11t2

.

A. Find the average velocity for the time period beginning when t=2

and lasting

.01 = -7.5611 (36-11x^2) x=2-.01

.005 =-7.780275 (36-11x^2) x=2-.005

.002 = -7.91912044 (36-11x^2) x=2-.002

.001 = -7.956011 (36-11x^2) x=2-.001

Estimate the instantaneous velocity when t=2.

Answer: = -8 (36-11x^2) x=2

In bold are the formulas that I used but the homework websites says part B is correct and part A are all wrong? What did I do wrong?

Answer 1

The problem is the formula you used for the average velocity over the time period.

It should be:

1. ( f(t₂) = f(t₁) ) / Δt, where Δt = t₂ - t₁
2. It is basically the slope between two points.

So, your first average should be:

1. ( 36(2.01) - 11(2.01)² ) - (36(2) - 11(2)² ) / 0.01 = -8.11
2. The others should be -8.055, -8.022, -8.011

The thing to keep in mind is that average velocity (or most any average rate) is essentially a slope of the line connecting the beginning point to the ending point.

Let m know if this was helpful,

David

Answer 2

You need to evaluate [y(2+h)-y(2)]/h for h = each of those small decimal values.