Calculas question help

Question

For each value below, enter the number correct to four decimal places.Suppose an arrow is shot upward on the moon with a velocity of 58 m/s, then its height in meters after  seconds is given by . Find the average velocity over the given time intervals.

[6, 7]:     

[6, 6.5]:     

[6, 6.1]:     

[6, 6.01]:     

[6, 6.001]:

Answer 1

To find the height at various times, just plug in the associated values of t into the function. For example at t = 6, the height is h(6) = 58(6) - 0.83(6)² = 348 - 29.88 = 318.12 m

Here is a table of values of "t" vs heights (or h(t)):

Time       Height

 (t)           (h(t))

6            318.12

6.001     318.1680392

6.01       318.600317

6.1         322.9157

6.5         341.9325

7            365.33

The average velocity is given by (h₂ - h₁)/(t₂ - t₁). For the interval [6, 7] the points are as follows:

(t₁, h₁) = (6, 318.12)

(t₂, h₂) = (7, 365.33)

So the average velocity is (365.33 - 318.12)/(7 - 6) = 47.12/1 = 47.1200 m/s

For the interval [6, 6.5] the points are:

(t₁, h₁) = (6, 318.12)

(t₂, h₂) = (6.5, 341.9325)

So the average velocity is: (341.9325 - 318.12)/(6.5 - 6) = 23.8125/0.5 = 47.6250 m/s

Just keep repeating the process for the other time intervals.