Pa and Oz start walking at the same corner of a field whose south- west is bounded by a straight wall. Pa walks alongside the wall at 5.5 km/h while Oz sets off at 6 km/h along a straight foot path across the field which makes an angle of 50 degrees with the wall. Find the velocity of Oz relative to Pa and their distance apart after 10 minutes.
To find the velocity of Oz relative to Pa, we need to find the horizontal and vertical components of Oz's velocity.
Let's start by finding the horizontal component of Oz's velocity. We can use trigonometry to find this component.
The angle between Oz's foot path and the wall is 50 degrees. The horizontal component of Oz's velocity can be found using the formula:
horizontal component = velocity * cos(angle)
Given that Oz's velocity is 6 km/h and the angle is 50 degrees, we can calculate the horizontal component:
horizontal component = 6 km/h * cos(50 degrees)
Next, let's find the vertical component of Oz's velocity. Using trigonometry again, we can find this component:
vertical component = velocity * sin(angle)
Given that Oz's velocity is 6 km/h and the angle is 50 degrees, we can calculate the vertical component:
vertical component = 6 km/h * sin(50 degrees)
Now, let's find the velocity of Oz relative to Pa. Since Pa is walking parallel to the wall, his velocity has no vertical component. Therefore, the velocity of Oz relative to Pa is equal to Oz's horizontal component.
velocity of Oz relative to Pa = horizontal component of Oz's velocity
Now, let's find their distance apart after 10 minutes. To do this, we need to calculate the distance each person has traveled in 10 minutes and subtract Pa's distance from Oz's distance.
Pa's distance = Pa's velocity * time
Given that Pa's velocity is 5.5 km/h and the time is 10 minutes (which can be converted to hours by dividing by 60), we can calculate Pa's distance:
Pa's distance = 5.5 km/h * (10 minutes / 60 minutes/hour)
Similarly, we can find Oz's distance:
Oz's distance = Oz's velocity * time
Given that Oz's velocity is 6 km/h and the time is 10 minutes (which can be converted to hours by dividing by 60), we can calculate Oz's distance:
Oz's distance = 6 km/h * (10 minutes / 60 minutes/hour)
Finally, we can find their distance apart after 10 minutes by subtracting Pa's distance from Oz's distance:
distance apart = Oz's distance - Pa's distance
Now you have the method to find the velocity of Oz relative to Pa and their distance apart after 10 minutes.