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3 years ago

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"A hiker starts at point P and walks 2.0 kilometers due east and then 1.4 kilometers due north. The vectors in the diagram below

represent these two displacements.
Using a metric ruler, determine the scale used in the vector diagram"

1 answer:

Law Incorporation [45]3 years ago

3 0

Here, you need to use your "Protractor" as it is given in the question, but we can calculate the value with the help of our mathematical calculation too:
[ Protractor can be use only in real life, not here ]

Draw an imaginary line from initial position to final position.
Now, In that triangle, tan x = P/B
tan x = 1.4 / 2
tan x = 0.70
x = tan⁻¹ (0.70)
x = 35 [ tan 35 = 0.70 ]

In short, Your Answer would be 35 degrees

Hope this helps!

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A car is being driven along a road at 25m/s when the driver suddenly notices that there is a fallen tree blocking the road 65m a

Anuta_ua [19.1K]

Hi there!

We can use the following equation to solve for displacement:

vf² = vi² + 2ad, where:

vf = final velocity

vi = initial velocity

a = acceleration

d = displacement

Since the car will come to rest, vf = 0, so:

0 = vi² + 2ad

Plug in the given values:

0 = 25² + 2(-5)d (Breaking is a negative acceleration in this instance)

Solve:

0 = 25² - 10d

10d = 625

d = 62.5m

Subtract from the total distance from the car to the tree:

65 - 62.5 = 2.5m

3 0

3 years ago

Two electric motors drive two elevators of equal mass in a three-story building 10 meters tall. Each elevator has a mass of 1,00

wlad13 [49]

Answer:

Power output = $2\times 10^4\ W$

Explanation:

Given:

Mass of the elevator is, $m=1000\ kg$

Height to which it is raised is, $h=10\ m$

Acceleration due to gravity is, $g=10\ m/s^2(Approximately)$

Time taken by the motor to raise the elevator is, $t=5.0\ s$

Now, work done on the elevator by the motor is equal to the increase in the gravitational potential energy of the elevator.

Increase in gravitational potential energy is given as:

$\Delta U=mgh=(1000)(10)(10)=10\times 10^4\ J$

Therefore, work done by motor is, $W=10\times 10^4\ J$

Now, we know that, power is work done in unit time. So, power output is given as:

$Power=\frac{W}{t}\\\\Power=\frac{10\times 10^4\ J}{5.0\ s}\\\\Power=2\times 10^4\ J/s\\\\Power=2\times 10^4\ W..........[1 W = 1\ J/s]$

Therefore, the power output of the first motor is $2\times 10^4\ W$

7 0

3 years ago

The wheel of a stationary exercise bicycle at your gym makes one rotation in 0.670 s. Consider two points on this wheel: Point P

lesya [120]

Answer:

a) For P: $v=0.938\frac{m}{s}$

For Q: $v = 1.876\frac{m}{s}$

b) For P:

$a_{rad}=8.80\frac{m}{s^{2}}$

for Q:

$a_{rad}=17.60\frac{m}{s^{2}}$

c) As the distance from the axis increases then speed increases too.

Explanation:

a) Assuming constant angular acceleration we can find the angular speed of the wheel dividing the angular displacement θ between time of rotation:

$\omega =\frac{\theta}{t}$

One rotation is 360 degrees or 2π radians, so θ=2π

$\omega =\frac{2\pi}{0.670} =9.38\frac{rad}{s}$

Angular acceleration is at every point on the wheel, but speed (tangential speed) is different and depends on the position (R) respect the rotation axis, the equation that relates angular speed and speed is:

$v = \omega R$

for P:

$v = 9.38\frac{rad}{s}*0.1m=0.938\frac{m}{s}$

for Q:

$v = 9.38\frac{rad}{s}*0.2m=1.876\frac{m}{s}$

b) Centripetal acceleration is:

$a_{rad}= \frac{v^2}{R}$

for P:

$a_{rad}= \frac{(0.938)^2}{0.1}=8.80\frac{m}{s^{2}}$

for Q:

$a_{rad}= \frac{(1.876)^2}{0.2}=17.60\frac{m}{s^{2}}$

c) As seen on a) speed and distance from axis is $v = \omega R$ because ω is constant the if R increases then v increases too.

3 0

3 years ago

A force of 12 N changes the momentum of a toy car from 3kgm/s t0 10kgm/s. Calculate the time the force took to produce this chan

yan [13]

Answer:

Time = 0.58 seconds

Explanation:

Given the following data;

Initial momentum = 3 kgm/s

Final momentum = 10 kgm/s

Force = 12 N

To find the time required for the change in momentum;

First of all, we would determine the change in momentum.

$Change \; in \; momentum = final \; momentum - initial \; momentum$

$Change \; in \; momentum = 10 - 3$

Change in momentum = 7 kgm/s

Now, we can find the time required;

Note: the impulse of an object is equal to the change in momentum experienced by the object.

Mathematically, impulse (change in momentum) is given by the formula;

$Impulse = force * time$

Making "time" the subject of formula, we have;

$Time = \frac {impulse}{force}$

Substituting into the formula, we have;

$Time = \frac {7}{12}$

Time = 0.58 seconds

6 0

3 years ago

In the first law of Thermodynamics ΔE = Q - W, what does ΔE stand for???

Alexxx [7]

<span>Δ</span>E = q + w

q = heat (quantity of)

q and w can be positive or negative depending on if work/heat is being absorbed/done on the system or released/done by the system

7 0

3 years ago

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