Mathematics: If a ball is thrown into the air with a velocity of 34 ft/s, its height in feet t seconds later is given by y = 34t − 16t2.(a) find the average velocity for the time period beginning when t = 2 and lasting for each of the following.(i) 0.5 seconds ft/s(ii) 0.1 seconds ft/s(iii) 0.05 seconds ft/s(iv) 0.01 seconds ft/s(b) estimate the instantaneous velocity when t = 2. ft/s

I think the answer is A. and F. I could be wrong ...

If a ball is thrown into the air with a velocity of

Ответ:

amahar4000

02.01.2022

Mathematics

(a). (i) $-38\ \frac{ft}{s}$ ; (ii) $-31.6\ \frac{ft}{s}$ ; (iii) $-30.8\ \frac{ft}{s}$ ; (iv) $-30.16\ \frac{ft}{s}$

(b). $-30\ \frac{ft}{s}$

Step-by-step explanation:

The formula you need to use is:

$V_{avg}=\frac{y_2-y_1}{t_2-t_1}$

Then, in this case:

$V_{avg}=\frac{(34t_2 -16(t_2)^2)-(34t_1 - 16(t_1)^2)}{t_2-t_1}$

(a) Susbtituting values, we get:

(i) $V_{avg}=\frac{(34(2.5) - 16(2.5)^2)-(34(2)- 16(2)^2)}{2.5-2})=-38\ \frac{ft}{s}$

(ii) $V_{avg}=\frac{(34(2.1) - 16(2.1)^2)-(34(2)- 16(2)^2)}{2.5-2})=-31.6\ \frac{ft}{s}$

(iii) $V_{avg}=\frac{(34(2.05) - 16(2.05)^2)-(34(2)- 16(2)^2)}{2.5-2})=-30.8\ \frac{ft}{s}$

(iv) $V_{avg}=\frac{(34(2.01) - 16(2.01)^2)-(34(2)- 16(2)^2)}{2.5-2})=-30.16\ \frac{ft}{s}$

(b) Observe that as the time after 2 second gets smaller, the average velocity gets closer to $-30\ \frac{ft}{s}$ . Therefpre, we can can estimate that the instantaneous velocity when t = 2 is:

$V=-30\ \frac{ft}{s}$

0,0(0 оценок)

Ответ:

Ответ:

Ask your question to the AI advisor

More tips

Answers on questions: Mathematics

Ask an AI advisor a question