A rubber band that has been stretched has gained ___

If |v|= 11, |w|= 23, |v-w|= 30, find |v+w|

GenaCL600 [577]

Answer:

$|v+w|=20$

Explanation:

We are given that

|v|=11

|w|=23

|v-w|=30

We have to find the value of |v+w|

|a-b|^2=(a+b)\cdot (a+b)=a^2+b^2-2|a||b|cos\theta

Using the formula

$(30)^2=(11)^2+(23)^2-2(11)(23)cos\theta$

$900=121+529-506cos\theta$

$900-121-529=-506cos\theta$

$250=-506cos\theta$

$cos\theta=-\frac{250}{506}$

$|a+b|^2=|a|^2+|b|^2+2a\cdot bcos\theta$

Using the formula

$|v+w|^2=(11)^2+(23)^2+2(11)(23)\times (-\frac{250}{506})$

$|v+w|^2=400$

$|v+w|^2=(20)^2$

$|v+w|=20$

7 0

3 years ago

What is the power generated by a 45 kg person who walks up a flight of 12 stairs, each 30 cm high, in 12 s?

Free_Kalibri [48]

The total distance covered by the person is 12 times the height of each stair:
$\Delta h=12 \cdot 30 cm=360 cm=3.60 m$

The work done by the person to climb the stairs is equal to the increase in his gravitational potential energy:
$W= \Delta U=mg \Delta h=(45 kg)(9.81 m/s^2)(3.60 m)=1589.2 J$

And therefore, the power generated by the person in 12 s is the work done divided by the time taken:
$P= \frac{W}{t}= \frac{1589.2 J}{12 s}=132.3 W$

So, the correct answer is B.

3 0

4 years ago

KI + Cl2 ---> KCl + I2<br> Balance the single replacement chemical reaction.

snow_lady [41]

Answer:

2KI + Cl₂ → 2KCl + I₂

Explanation:

The reaction equation is given as:

KI + Cl₂ → KCl + I₂

The problem at hand is to balance this chemical reaction. To solve this problem we use a mathematical approach;

aKI + bCl₂ → cKCl + dI₂

Conserving K : a = c

I : a = 2d

Cl : 2b = c

Now let a = 1, c = 1 , d = $\frac{1}{2}$ , b = $\frac{1}{2}$ , ;

Multiply through by 2;

a = 2, b = 1 , c = 2, d = 1

2KI + Cl₂ → 2KCl + I₂

5 0

3 years ago

A 2.1 kg steel ball strikes a massive wall at 13.2 m/s at an angle of 64.8 ◦ with the perpendicular to the plane of the wall. It

solong [7]

Answer:

112 N

Explanation:

going through the question you would notice that some detail is missing, using search engines u was able to find a similar question on "https://socratic.org/questions/a-2-3-kg-steel-ball-strikes-a-wall-with-a-speed-of-8-5-m-s-at-an-angle-of-64-wit"

and here is the question i found

"A 2.3 kg steel ball strikes a wall with a speed of 8.5 m/s at an angle of 64⁰ with the surface. It bounces off with the same speed and angle. If the ball is in contact with the wall for 0.448 s. What is the average force exerted by the ball?"

you would notice that there is a change in the values from the question posted, hence we would only take the following part to complete our question, " If the ball is in contact with the wall for 0.448 s what is the average force exerted by the ball?" while retaining all original detail.

solution

mass of ball (m) = 2.1 kg

speed of ball (v) = 13.2 m/s

angle of contact (p) = 64.8°

time of contact (t) = 0.448 s

What is the average force exerted by the ball?

The average force exerted by the ball = $\frac{change in momentum}{change in time}$

where

The momentum changes only the direction perpendicular to the wall, hence the component of momentum perpendicular to the wall = m x v x sin (p) = 2.1 x 13.2 x sin 64.8 = 25.1 kg.m/s

since the ball strikes the wall and bounces off it with the same speed

and at the same angle, the component of momentum acting

perpendicular to the wall remains the same while hitting and leaving

the wall but in opposite directions.

Hence the component of momentum acting perpendicular to the wall while hitting and leaving the wall will be 25.1 kg.m/s and -25.1 kg.m/s respectively.

change in momentum = 25.1 - (-25.1) = 25.1 + 25.1 = 50.2 kg.m/s

change in time = 0.448 s

now substituting the above into the equation we have

The average force exerted by the ball = $\frac{50.2}{0.448}$ = 112 N

6 0

3 years ago

How could you work out the direction that the motor will turn

IgorLugansk [536]

If you mean work out as in using calculations, I don't know how to help you. But there is a way to find out, using Fleming's left hand rule. I can't define it properly, and I don't want to copy-paste from another site, so I strongly recommend that you look it up. Try google, or more specific, BBC GCSE bitesize.

Hope this helps!

5 0

3 years ago

Read 2 more answers

A rubber band that has been stretched has gained ____ energy