In a total time of 25s, a field hockey player runs 25 m [26 degrees N of E] and then runs 32 m [18 degrees S of E] determine her average velocity.
To determine the average velocity of the field hockey player, we need to calculate the total displacement and divide it by the total time taken.
First, we need to find the horizontal and vertical components of each displacement.
For the first displacement of 25 m at 26 degrees N of E:
- Horizontal component: 25 m * sin(26 degrees)
- Vertical component: 25 m * cos(26 degrees)
For the second displacement of 32 m at 18 degrees S of E:
- Horizontal component: 32 m * sin(18 degrees)
- Vertical component: -32 m * cos(18 degrees) [negative because it is in the opposite direction]
Next, calculate the sum of the horizontal and vertical components for both displacements.
Horizontal component: (25 m * sin(26 degrees)) + (32 m * sin(18 degrees))
Vertical component: (25 m * cos(26 degrees)) + (-32 m * cos(18 degrees))
Now, we can calculate the total displacement using the formula:
Total displacement = sqrt((horizontal component)^2 + (vertical component)^2)
Finally, divide the total displacement by the total time taken to find the average velocity.
Average velocity = Total displacement / Total time (25 seconds)
Substitute the values into the formula to find the average velocity.