The lion first runs 200 yards at 20 deg. south of west, then 300 yards at 40 deg. west of north, and finally 400 yards at 10 deg east of north at which point it catches up to the deer. How far from the starting point, and in what direction is the point where the lion and the deer meet?

Question

The lion first runs 200 yards at 20 deg. south of west, then 300 yards at 40 deg. west of north, and finally 400 yards at 10 deg east of north at which point it catches up to the deer. How far from the starting point, and in what direction is the point where the lion and the deer meet?

How do I set up the problem?

Answer 1

set the staring point at (0,0)

Now, figure the relative displacement of each leg of the trip:

(200 cos(180-20)°, 200 sin(180-20)°)
(300 cos(90+40)°, 300 sin(90+40)°)
(400 cos(90-10)°, 400 sin(90-10)°)

Now just add up the x- and y-displacements to get the final location.

Answer 2

To set up this problem, we can use vector addition to find the total displacement of the lion. We need to determine the direction and magnitude of each individual displacement for the lion.

Let's break down the given information:

- The lion first runs 200 yards at 20 degrees south of west. This means the angle between its path and the west direction is 20 degrees, and the magnitude (length) of this displacement is 200 yards.
- The second displacement is 300 yards at 40 degrees west of north. This means the angle between its path and the north direction is 40 degrees, and the magnitude of this displacement is 300 yards.
- The third displacement is 400 yards at 10 degrees east of north. This means the angle between its path and the north direction is 10 degrees east, and the magnitude of this displacement is 400 yards.

Now, let's calculate the x and y components of each displacement using trigonometry.

For the first displacement (200 yards at 20 degrees south of west):
- The x-component (west direction) is given by: 200 yards * cos(20 degrees).
- The y-component (south direction) is given by: 200 yards * sin(20 degrees).

For the second displacement (300 yards at 40 degrees west of north):
- The x-component (west direction) is given by: 300 yards * cos(40 degrees).
- The y-component (north direction) is given by: 300 yards * sin(40 degrees).

For the third displacement (400 yards at 10 degrees east of north):
- The x-component (north direction) is given by: 400 yards * sin(10 degrees).
- The y-component (east direction) is given by: 400 yards * cos(10 degrees).

Once we have calculated the x and y components for each displacement, we can add them together to find the total x and y components of the lion's displacement. Finally, we can use the Pythagorean theorem and trigonometry to find the magnitude and direction of the point where the lion and the deer meet.