Question

If an arrow is shot upward on Mars with a speed of 56 m/s, its height in meters t seconds later is given by y = 56t − 1.86t2.

(a) Find the average speed over the given time intervals.
(i) [1, 2] m/s
(ii) [1, 1.5] m/s
(iii) [1, 1.1] m/s
(iv) [1, 1.01] m/s
(v) [1, 1.001] m/s
(b) Estimate the speed when t = 1. m/s.

Answer 1

Answer: (a) (i)50.42 m/s (ii) 51.35 m/s (iii) 52.094 m/s (iv) 52.2614 m/s (v) 52.27814 m/s

(b) 54.14 m/s

Explanation:

The average speed over the given time interval [a,b]: =
`(y(b)-y(a))/(b-a)`

Given: If an arrow is shot upward on Mars with a speed of 56 m/s, its height in meters t seconds later is given by
`y = 56t − 1.86t^2.`

(a)

(i) average speed =
`(y(2)-y(1))/(2-1)`

`=(56(2)-1.86(2)^2-(56(1)-1.86(1)^2))/(1)`

`=50.42` m/s

(ii) average speed =
`(y(1.5)-y(1))/(1.5-1)`

`=(56(1.5)-1.86(1.5)^2-(56(1)-1.86(1)^2))/(0.5)`

`=51.35`m/s

(iii) average speed =
`(y(1.1)-y(1))/(1.1-1)`

`=(56(1.1)-1.86(1.1)^2-(56(1)-1.86(1)^2))/(0.1)`

`=52.094`m/s

(iv) average speed =
`(y(1.01)-y(1))/(1.01-01)`

`=(56(1.01)-1.86(1.01)^2-(56(1)-1.86(1)^2))/(0.01)`

`=52.2614`m/s

(v) average speed =
`(y(1.001)-y(1))/(1.001-01)`

`=(56(1.001)-1.86(1.001)^2-(56(1)-1.86(1)^2))/(0.001)`

`=52.27814`m/s

(b)
`y(1)=56(1)-1.86(1)^2`

`=56-1.86`

`= 54.14` m/s