An airplane flying at 600 miles per hour has a bearing of 152 degrees. After flying for 1.5 hours, how far north and how far east will the plane have traveled from point of departure?

bearing relative to N, clockwise?

The plane is going S, not N.

East: 600*1.5 sin152

N: 600*1.5*cos152 (notice cosine will be -, making the N distance -, or + S.)

a plane with airspeed of 450 miles per hour is flying in the direction N35 degress west?

To find out how far north and how far east the plane will have traveled, we need to use some trigonometry and the concept of vectors.

First, let's break down the problem. The plane is flying at 600 miles per hour, and its bearing is 152 degrees. This means that it is moving at an angle of 152 degrees with respect to the north.

To find the distance traveled in 1.5 hours, we can multiply the speed of the plane (600 miles per hour) by the time (1.5 hours):
Distance = Speed × Time
Distance = 600 miles/hour × 1.5 hours
Distance = 900 miles

Now, let's calculate how far north and how far east the plane will have traveled from the point of departure.

To determine the northward component, we use the formula:
Northward distance = Distance × sin(bearing)

To determine the eastward component, we use the formula:
Eastward distance = Distance × cos(bearing)

Now, let's plug in the values and calculate.

Northward distance = 900 miles × sin(152 degrees)
Northward distance ≈ -733.36 miles (rounded to the nearest hundredth)

Eastward distance = 900 miles × cos(152 degrees)
Eastward distance ≈ 403.80 miles (rounded to the nearest hundredth)

Therefore, the plane will have traveled approximately -733.36 miles north (rounded to the nearest hundredth) and 403.80 miles east (rounded to the nearest hundredth) from the point of departure. The negative sign indicates a southward direction for the northward component.