Which number line shows the graph of -3?

A canister is dropped from a helicopter 500m above the ground. Its parachute does not open, but the canister has been designed t

solmaris [256]

Answer:

The impact speed 98.995 m/s is less than 100 m/s and the canister will not burst.

Step-by-step explanation:

A function F is called an antiderivative of f on an interval I if $F'(x) = f(x)$ for all x in I.

Recall that if the object has position function $s=f(t)$ , then the velocity function is $v(t)=s'(t)$ . This means that the position function is an antiderivative of the velocity function. Likewise, the acceleration function is $a(t)=v'(t)$ , so the velocity function is an antiderivative of the acceleration.

An object near the surface of the earth is subject to a gravitational force that produces a downward acceleration denoted by $g$ . For motion close to the ground we may assume that $g$ is constant, its value being about $9.8 \:{\frac{m}{s^2}}$ .

We know that the acceleration due to gravity is given by

$a(t)=-9.8$

and the antiderivative is velocity

$v(t)=\int a(t)\,dt\\v(t)=\int -9.8\,dt\\v(t)=-9.8t +C$

We know that the canister was dropped, so the initial velocity at t = 0 is zero, this fact let us know the value of C.

$v(0)=9.8(0)+C\\C=0$

The antiderivative of velocity is the position

$s(t)=\int v(t) \, dt\\s(t)=\int -9.8t \, dt\\s(t)=-4.9t^2+C$

To find the value of the constant C, we know that the height was 500 m at t = 0, this means $s(0)=500$

$500=-4.9(0)^2+C\\C=500$

$s(t)=-4.9t^2+500$

Using the fact that at the time of impact the height s(t) is zero we can compute the total time of the fall:

$s(t)=-4.9t^2+500=0\\\\-4.9t^2=-500\\\\t^2=\frac{5000}{49}\\\\\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\\\t=\sqrt{\frac{5000}{49}},\:t=-\sqrt{\frac{5000}{49}}$

A negative time does not make sense, so we only take as a possible solution

$t=\sqrt{\frac{5000}{49}}=\frac{50\sqrt{2}}{7}\approx 10.102$

Now the final velocity is

$v(\frac{50\sqrt{2}}{7})=-9.8(\frac{50\sqrt{2}}{7})\approx -98.995$

The impact speed 98.995 m/s is less than 100 m/s and the canister will not burst.

5 0

3 years ago

Can someone help me please

lina2011 [118]

As it is a parallelogram,
z = 124°
x = 180°-124°-33°
= 23°
y = 33°

4 0

3 years ago

Please help me with this question and can u please do it on paper and take a pic of it. Thank You!

Likurg_2 [28]

click on pics click on pics

GodBless c:

4 0

3 years ago

The Murphy family is on a road trip. On the first day, they traveled 30% of their total distance. On the second day, they travel

olga_2 [115]

Answer:

$\frac{11}{20}$

On the first day, they traveled 30 percents of the total distance. On the second day they traveled one fourth of the total distance. One fourth converted into percentage is 25 percent. Then you add 30 plus 25 because that is the to a

total distance that Murphy's family traveled for 2 days. It will be 55 percents, and you convert 55 percents into fraction will be 55/100, and you simplify it, will be 11/20.

7 0

3 years ago

HELP! 8TH GRADE MATH PLS LOL

LekaFEV [45]

<h2>Given:-</h2>

${ \large{➢ \: \: \bf{x = - 8}}}$