Vectors. Adding, subtracting, and velocity questions

[Matt12345]

So I have a few problems that I need help with. Any help would be greatly appreciated as I am new here and stumped.

1. A woman walks 220 m in the direction 27 degrees east of north, then 205 m directly east.
(a) find the magnitude (finished it).
362.5 m

(b) Find the angle of her final displacement from the starting point.
?

(c) Find the distance she walks (finished it).
425

2. Suppose a-b=2c, a+b=9c, and c=5i+3j. (***NOTE: all "a","b", and "c" have directional arrows above them I just didn't know how to put them there. The i and j have ^ above them as well).

(a). What is a?
?

(b). What is b?

5. At one instant a bicyclist is 35 m due east of a park's flagpole, going due south with a speed of 11 m/s. Then, 12 s later, the cyclist is 50 m due north of the flagpole, going due east with a speed of 12 m/s. For the cyclist in this 12 s interval, find each of the following.

(a) displacement (solved)
magnitude = 61 m
direction = 55 degrees north of west

(b) average velocity (solved)
magnitude =5.08 m/s
direction = 55 degrees north of west

(c) average acceleration
magnitude = ? m/s^2
direction = ? degrees north of east

6. A ball rolls horizontally off the edge of a tabletop that is 2.00 m high. It strikes the floor at a point 1.57 m horizontally away from the table edge. (Neglect air resistance.)

(a) How long was the ball in the air?
? s

(b) What was its speed at the instant it left the table.
?


I am sorry there are so many, I got the majority of them but was very confused on these. At first I thought I new how to do 6 but then I realized that I didn't have the instant velocity in the x direction. All help is greatly appreciated. Thanks again.

 

[Matt12345]

I have answered all except question 5 part c. I got the acceleration, and the angle, but I cannot figure out the magnitude of the average acceleration. Any help?

 

[kerimek]

I am happy to assist you with these problems related to vectors, adding, subtracting, and velocity. These concepts are fundamental in physics and understanding them will help you in solving more complex problems in the future.

Let's start with problem 1. The woman's final displacement can be found by adding her two displacements together using vector addition. This can be done by breaking each displacement into its x and y components and then adding them separately. Once you have the final x and y components, you can use the Pythagorean theorem to find the magnitude and the inverse tangent function to find the angle.

For problem 2, we can use the given equations to solve for a and b. To do this, we will substitute the value of c (5i+3j) into the equations and then solve for a and b. This will give us the magnitude and direction of both a and b.

In problem 5, we can use the given information to find the displacement, average velocity, and average acceleration of the cyclist. To find the average acceleration, we can use the formula a = (Vf - Vi)/t, where Vf is the final velocity, Vi is the initial velocity, and t is the time. We can use the Pythagorean theorem and inverse tangent function to find the magnitude and direction of the displacement and average velocity.

Lastly, for problem 6, we can use the kinematic equations to solve for the time and initial velocity of the ball. Since the ball is rolling horizontally, we can assume that there is no initial velocity in the y direction. This means that we only need to solve for the initial velocity in the x direction. Once we have the initial velocity, we can use the formula d = V0t + 1/2at^2 to solve for the time.

I hope this helps you understand and solve these problems. Remember to break the vectors into their components and use the appropriate equations to solve for the unknowns. If you still have trouble, don't hesitate to ask for further clarification or assistance. Good luck!