Mathematics, 30.01.2020 16:05 castiaulii16

An arrow is shot vertically upward at a rate of 180ft/s. use the projectile formula h=? 16t2+v0t to determine at what time(s), in seconds, the arrow is at a height of 420ft. round your answer(s) to the nearest tenth of a second.

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Answer from: samanthasheets8006

Hello!

The answer is:

$t_1=3.60s\\t_2=7.94s$

Time equal to 3.30 seconds when the arrow was going up.

Time time equal to 7.94 seconds when the arrow was going down.

Why?

To solve the problem, we need to solve the quadratic equation and find the value of values of time where the height of the arrow is 420 feet.

Also, we are given some information, we need to substitute it and then use the quadratic equation.

The equation is:

$h=-16t^{2}+vot\\\\-16t^{2}+vot-h=0$

Substituting the given information we have:

$-16t^{2}+vot-h=0$

$-16t^{2}+180\frac{ft}{s} t-420=0$

We have a quadratic equation where:

$a=-16\\b=180\\c=-420$

Now, using the quadratic equation to find the value or values of "t", we have:

$\frac{-b+-\sqrt{b^{2}-4ac } }{2a}$

$\frac{-180+-\sqrt{180^{2}-4*-16*-420 } }{2*-16}=\frac{-180+-\sqrt{32400-26880 } }{-32}\\\\\frac{-180+-\sqrt{32400-26880}}{-32}=\frac{-180+-\sqrt{5520}}{-32} \\\\\frac{-180+-\sqrt{5520}}{-32}=\frac{-180+-(74.29)}{-32}\\\\t_1=\frac{-180+(74.29)}{-32}=3.30\\\\t_2=\frac{-180-(74.29)}{-32}=7.94$

Hence, we have two positive values of time, it means that there are two moments of time where the height of the arrow is equal to 420 feet, those times are:

$t_1=3.60s\\t_2=7.94s$

Time equal to 3.30 seconds when the arrow was going up.

Time equal to 7.94 seconds when the arrow was going down.

Have a nice day!

Answer from: Quest

eww xbox also eww dayz

step-by-step explanation:

just for that im not answering

Add me on xbox @ xxvaporizexxxx been grinding dayz lol also answer this

Answer from: Quest

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺

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