6. using trigonometry, solve for the x and y components of the following: a. 17.0 m/s @ 30.0o c. 13.0 m/s2 @ 120o b. [email  protected] d. 22.0m/[email  protected] 7. usingthecomponentsbelow, calculate its magnitude and direction. a. ax =34.0m, ay =-34.0m b. bx =0.00km, by =150.0km c. cx = -8.00 m/s2, cy = 6.00 m/s2 8. a girl holds a stick at an angle with one end on the ground and the other end 0.750 m above the ground. the sun shines straight downward on the stick, and the stick makes a shadow on the ground that is 1.25 m long. what is the length of the stick and the angle it makes with the ground? 9. a boat travels on a heading of 40.0o north of east for a distance of 300 km. how far north and how far east of its starting point does the boat sail? 10.a weather station releases a weather balloon. the balloon’s buoyancy accelerates it upward at 15 m/s2. at the same time, a wind accelerates it horizontally to the right at 6.5 m/s2. what is the resulting acceleration? 11.using the analytical method of vector addition, sketch and solve the following: a. [email  protected] [email  protected] b. 22.0 m/s @ 225o + 40.0 m/s @ 315o c. 17.0 m/s2 @ 330o - 11.0 m/s2 @ 270o 12.a car travels along a curved section of road. initially the car has velocity 30.0 m/s @ 90.0o. after 5.00 s the car has a velocity of 30.0 m/s @ 95.0o. a. calculate the change in the car's velocity. b. calculate the car's average acceleration.

i have all of the answers already, but i need to show work. if you could pls show the work for me that would be such a !

6a) Vector: 17.0 m/s @

x-component:

y-component:

6b) Vector: 13.0 m/s^2 @

x-component:

y-component:

6c) Vector: 19.0 m @

x-component:

y-component:

6d) Vector: 22.0 m/s @

x-component:

y-component:

7a) Components: Ax =34.0m,Ay =-34.0m

Magnitude:

Direction:

7b) Components: Bx =0.00km,By =150.0km

Magnitude:

Direction: since it is in the y-direction (no component on x)

7c) Components: Cx = -8.00 m/s2, Cy = 6.00 m/s2

Magnitude:

Direction:

8) In this problem, 0.750 m corresponds to the vertical side and 1.25 m corresponds to the horizontal side of a right triangle. The length of the stick corresponds to the length of the hypothenuse of this triangle, that can be found using the Pytagorean's theorem:

The angle the stick makes with the ground is given by:

9) The displacement of the boat corresponds to a vector of length L=300 km and angle with respect to east. Therefore, the two components in the north and east directions are:

- north:

- east:

10) The two accelerations correspond to the two sides of a right triangle, therefore the resultant acceleration corresponds to the length of the hypothenuse of the triangle:

11a) [email protected] [email protected]

Let's resolve each vector in its components:

Now we sum the components in each direction:

So the magnitude of the resultant vector is:

And the direction is:

11b) 22.0 m/s @ 225o + 40.0 m/s @ 315o

Let's resolve each vector in its components:

Now we sum the components in each direction:

So the magnitude of the resultant vector is:

And the direction is:

11c) 17.0 m/s2 @ 330o - 11.0 m/s2 @ 270o

Let's resolve each vector in its components:

Now we calculate the difference between the components in each direction:

So the magnitude of the resultant vector is:

And the direction is:

12a) The change in velocity is equal to the vector difference between the final velocity (vf) and the initial velocity (vi), so let's proceed as in the previous exercise:

Difference:

Magnitude of the resultant vector:

12b) Acceleration:

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explanation:

d) physical means can be used to separate the components of air.