need help with this physics questions
a jogger runs with a velocity of 6km/h 25 degrees north west for 35 minutes and then changes direction , jogging for 20 minutes at 4.5km/h 65 degrees east of north. using a vector diagram determine the joggers total displacement and his average velocity for the workout.
To solve this question, we need to break down the jogger's motion into its components and then combine them using vector addition.
Step 1: Determine the components of the first leg of the jogger's motion.
The jogger runs with a velocity of 6 km/h at an angle of 25 degrees northwest for 35 minutes. To find the components, we need to resolve the velocity into its north and west components.
The north component can be found using the formula:
North Component = Velocity * sin(angle)
North Component = 6 km/h * sin(25 degrees)
The west component can be found using the formula:
West Component = Velocity * cos(angle)
West Component = 6 km/h * cos(25 degrees)
Step 2: Determine the displacement for the first leg.
To find the displacement, we need to multiply the components obtained in Step 1 by the time duration (35 minutes).
Displacement in the north direction = North Component * time
Displacement in the west direction = West Component * time
Step 3: Repeat steps 1 and 2 for the second leg of the jogger's motion.
The jogger runs at a velocity of 4.5 km/h at an angle of 65 degrees east of north for 20 minutes. Follow the same steps to find the north and east components and then calculate the displacement.
Step 4: Add the displacements from the two legs together.
To find the total displacement, add the displacements obtained from Step 2 and Step 3.
Total Displacement in the north direction = Displacement from the first leg + Displacement from the second leg (Remember to consider the directions)
Total Displacement in the east direction = Displacement from the second leg
Step 5: Calculate the magnitude and direction of the total displacement.
Use the Pythagorean theorem to find the magnitude of the total displacement:
Magnitude of Total Displacement = square root of [(Total Displacement in the north direction)^2 + (Total Displacement in the east direction)^2]
To find the direction, use the inverse tangent (tan^(-1)) function:
Direction of Total Displacement = tan^(-1) [(Total Displacement in the east direction) / (Total Displacement in the north direction)]
Step 6: Calculate the average velocity.
Use the formula for average velocity:
Average Velocity = Total Displacement / Total Time
Since the total time is the sum of the times for the two legs of the jogger's motion, Average Velocity = Total Displacement / (35 minutes + 20 minutes)
By following these steps, you should be able to determine the jogger's total displacement and average velocity for the workout using a vector diagram.