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svp [43]
2 years ago
11

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.

Mathematics
1 answer:
Zina [86]2 years ago
3 0

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

Step-by-step explanation:

The average speed over the given time interval [a,b]: = \frac{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 = \frac{y(2)-y(1)}{2-1}

=\frac{56(2)-1.86(2)^2-(56(1)-1.86(1)^2)}{1}

=50.42 m/s

(ii) average speed = \frac{y(1.5)-y(1)}{1.5-1}

=\frac{56(1.5)-1.86(1.5)^2-(56(1)-1.86(1)^2)}{0.5}

=51.35m/s

(iii) average speed = \frac{y(1.1)-y(1)}{1.1-1}

=\frac{56(1.1)-1.86(1.1)^2-(56(1)-1.86(1)^2)}{0.1}

=52.094m/s

(iv) average speed = \frac{y(1.01)-y(1)}{1.01-01}

=\frac{56(1.01)-1.86(1.01)^2-(56(1)-1.86(1)^2)}{0.01}

=52.2614
m/s

(v) average speed = \frac{y(1.001)-y(1)}{1.001-01}

=\frac{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

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