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MissTica
3 years ago
12

The two vectors and in fig. 3-28 have equal magnitudes of 10.0 m and the angles are 30° and 105°. find the (a) x and (b) y compo

nents of their vector sum , (c) the magnitude of , and (d) the angle makes with the positive direction of the x axis.
Physics
1 answer:
mylen [45]3 years ago
6 0

You can just use basic trigonometry to solve for the x & y components.

<span>vector a = 10cos(30) i + 10sin(30) j = <5sqrt(3), 5></span>

vector b is only slightly harder because the angle is relative to vector a, and not the positive x-axis. Anyway, this just makes vector b with an angle of 135deg to the positive x-axis.

<span>vector b = 10cos(135) i + 10sin(135) j = <-5sqrt(2), 5sqrt(2)></span>

So now we can do the questions:

r = a + b

r = <5sqrt(3)-5sqrt(2), 5+5sqrt(2)>

(a) 5sqrt(3)-5sqrt(2)

(b) 5+5sqrt(2)

(c)

|r| = sqrt( (5sqrt(3)-5sqrt(2))2 + (5+5sqrt(2))2 )

= 12.175

(d)

θ = tan-1 ( (5+5sqrt(2)) / (5sqrt(3)-5sqrt(2)) )

θ = 82.5deg

<span> </span>

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A cyclist maintains a constant velocity of 4.1 m/s headed away from point A. At some initial time, the cyclist is 244 m from poi
astra-53 [7]

Answer:

d=490\ m is his final displacement from the point A after 60 seconds.

Explanation:

Given:

Cyclist is moving away from A.

  • velocity of cyclist, v=4.1\ m.s^{-1}
  • displacement of the cyclist from point A at the time of observation, d_i=244\ m
  • time after which the next observation is to be recorded, t=60\ s

Now as the cyclist is moving away from point A his change in displacement after the mentioned time:

\Delta d=v.t

\Delta d = 4.1 \times 60

\Delta d=246\ m

<u>Now the the final displacement from point A after the mentioned time:</u>

d=d_i+\Delta d

d=244+246

d=490\ m

6 0
3 years ago
An object of mass m has these three forces acting on it (there is no normal force, "no surface"). F1 = 5 N, F2 = 8 N, and F3 = 5
DIA [1.3K]

The figure is missing: find it in attachment.

a) (3i - 5j) N

First of all, we have to write each force as a vector with a direction:

- Force F1 points downward, so along the negative y-direction, so we can write it as

F_1 = -5 j

- Force F2 points to the right, so along the positive x-direction, so we can write it as

F_2 = +8 i

- Force F3 points to the left, so along the negative x-direction, so we can write it as

F_3 = -5 i

Now we can write the net force, by adding the three vectors and separating the x-component from the y-component:

F=F_1+F_2+F_3 = -5j+8i-5i = (8-5)i+(-5)j=(3i-5j)N

b) 5.8 N

The magnitude of the net force can be calculated by applying Pythagorean's theorem on the components of the net force:

F=\sqrt{F_x^2+F_y^2}

where

F_x = 3 N is the x-component

F_y = -5 N is the y-component

Substituting into the equation,

F=\sqrt{(3)^2+(-5)^2}=5.8 N

c) -59.0^{\circ}

The angle of the net force, measured with respect to the positive x-axis (counterclockwise), can be calculated by using the formula

\theta=tan^{-1} (\frac{F_y}{F_x})

where

F_x = 3 N is the x-component

F_y = -5 N is the y-component

Substituting into the equation, we find

\theta = tan^{-1} (\frac{-5}{3})=-59.0^{\circ}

d) 0.84 m/s^2

The acceleration can be found by using Newton's second law:

F=ma

where

F is the net force on an object

m is its mass

a is the acceleration

For the object in the problem, we know

F = 5.8 N

m = 6.9 kg

Solving the equation for a, we find the magnitude of the acceleration:

a=\frac{F}{m}=\frac{5.8}{6.9}=0.84 m/s^2

4 0
3 years ago
What is the amplitude and wavelength of the wave shown below?
masha68 [24]

Answer:

Option B

Explanation:

I did a question like this a long time ago so i'm not sure if its right so sorry if its wrong

3 0
3 years ago
In an elastic collision, two objects collide and return to their original positions with no loss of _________.
BARSIC [14]
No loss of kinetic energy! :)
6 0
3 years ago
How are doctors both accurate and precise when preforming surgery or other things?
mr Goodwill [35]

Answer:

learning about the different functions of the body and therefore they have enough practice in order to have a clean and safe operation

Explanation:

4 0
3 years ago
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