Two planes take off from the same airport at the same time using different runways. One plane travels on a bearing S14 degrees W at 350 miles per hour. The other plane travel on a bearing N75 degrees E at 300 miles per hour. How far are the plane from each other 2 hours after takeoff?
How about you try one of these, and show how far you get?
Use the law of cosines for this one.
Given: AB = 300 m/h[75o]CW
AC = 350mi/h[94o]CW
AB = 600mi[75o]CW. BA = 600mi[75+180]CW
BC = BA+AC = 600mi[255o]CW+700mi[94o]
BC = (600*sin255+700*sin94)+(600*cos255+700*cos94)i
BC = 119-204i = 236[-30.3] = 236mi[330o]CW. = distance bet. planes.
To find the distance between the two planes after 2 hours, we can use the concept of relative velocity.
First, let's break down the given information:
Plane 1:
- Bearing: S14°W
- Speed: 350 miles per hour
Plane 2:
- Bearing: N75°E
- Speed: 300 miles per hour
To calculate the distance between the planes, we need to find the distance traveled by each plane in the respective directions after 2 hours.
Plane 1:
Since it is traveling in a southwesterly direction (S14°W), we can break down its velocity into its northward and westward components using trigonometry.
The northward component can be calculated by multiplying the speed (350 mph) by the sine of the angle (14°):
northward component = 350 * sin(14°)
The westward component can be calculated by multiplying the speed (350 mph) by the cosine of the angle (14°):
westward component = 350 * cos(14°)
Similarly, for Plane 2:
Since it is traveling in a northeasterly direction (N75°E), we can break down its velocity into its northward and eastward components using trigonometry.
The northward component can be calculated by multiplying the speed (300 mph) by the sine of the angle (75°):
northward component = 300 * sin(75°)
The eastward component can be calculated by multiplying the speed (300 mph) by the cosine of the angle (75°):
eastward component = 300 * cos(75°)
Now, to find the distance between the planes after 2 hours, we need to add the distances traveled in the northward and eastward directions.
Distance between the planes = square root((northward component of plane 1 - northward component of plane 2)^2 + (eastward component of plane 1 - eastward component of plane 2)^2)
After performing the calculations, the resulting distance will give us the answer.