Solve Vector Physics Problem: Displacement, Velocity, & Acceleration

[btchrist24]

1. An off-roader explores the open desert in her Hummer. First she drives 25 degrees west of north with a speed of 6.5 km/h for 15 minutes, then due east with a speed of 13 km/h for 7.5 minutes. She completes the final leg of her trip in 22 minutes.

a) What is the direction and speed of travel on the final leg? (Assume her speed is constant on each leg, and that she returns to her starting point at the end of the final leg.)

Theta= _______ degrees south of west

b) Express your answer using two significant figures.

v= ________ km/h

2.
Displacement Vector: Delta R; Delta R= Rf - Ri
Velocity Vector: POints in the direction of motion and has a magnitude equal to the speed.
Acceleration Vector: The acceleration vector indicated how quickly and in what direction the velocity is changing. It need not point in the direction of motion.
Velocity of Object 1 Relative to Object 3
V13= V12 + V23 where object 2 can be anything
Reversing the subscripts on a velocity
V12= -V21
3. I am really lost on this problem. I began by drawing a graphical representation. If the off-roader heads 25 degrees west of north, it would be 25 degrees to the left of the 90 degrees on the graph, which would equate to 90 deg + 25 deg. = (+) 115 degrees. I think you have to get a delta V (velocity) by subtracting Vf - Vi. I am really lost at this point. A general outline of how to approach this problem would be great!

 

[Kurdt]

Welcome to PF btchrist. Could I just ask you to re-post the question as you have it written down. It is a little unclear what must be done to find the final leg of the journey. Secondly, when posting any value please supply the appropriate units with it. It makes things a lot clearer and easier to deal with as it saves guessing what numbers are.

 

[m2003]

Hello, thank you for reaching out. Solving vector physics problems can be challenging, but with a systematic approach, it can become easier. Here is a general outline on how to approach this particular problem:

1. Draw a diagram: As you mentioned, drawing a graphical representation is a good first step. Make sure to label the different legs of the trip and the angles involved.

2. Break down the problem: The first leg of the trip is 15 minutes, the second leg is 7.5 minutes, and the final leg is 22 minutes. You can break down each leg into its individual components (displacement, velocity, and acceleration) and then combine them to find the overall displacement, velocity, and acceleration of the final leg.

3. Find the displacement: To find the displacement, you can use the formula Delta R = Rf - Ri. In this case, the final position (Rf) is the same as the initial position (Ri) since the off-roader returns to her starting point. So the displacement will be zero.

4. Find the velocity: To find the velocity, you can use the formula V = d/t, where d is the distance and t is the time. For the first leg, the distance is 6.5 km/h for 15 minutes, which can be converted to 0.25 hours. So the velocity for the first leg would be 6.5 km/h / 0.25 h = 26 km/h. Similarly, for the second leg, the velocity would be 13 km/h / 0.125 h = 104 km/h. For the final leg, the velocity would be the total distance (zero) divided by the total time (22 minutes, which is 0.367 hours). So the velocity for the final leg would also be zero.

5. Find the acceleration: To find the acceleration, you can use the formula a = (Vf - Vi) / t, where Vf is the final velocity, Vi is the initial velocity, and t is the time. For the first leg, the acceleration would be (26 km/h - 0 km/h) / 0.25 h = 104 km/h^2. For the second leg, the acceleration would be (104 km/h - 26 km/h) / 0.125 h = 624 km/h^2. For the final leg, the acceleration would be (0