A plane flies 230 mph at 60 degrees north of west for 2.5 hours
how far did the plane travel?
how far west did it go?
how far north did it go?
how fast did it go west?
A. D = 230mi/h * 2.5h = 575 mi.
B. Dx = 575*Cos60 =
C. Dy = 575*sin60 =
D. Vr = 575mi[60o]/2.5h = Resultant velocity.
Vx = Vr*Cos60 =
575 mi
To find the distance traveled by the plane, we can use the formula:
Distance = Speed × Time
Given that the plane flies at a speed of 230 mph for 2.5 hours, we can calculate the distance:
Distance = 230 mph × 2.5 hours = 575 miles
Therefore, the plane traveled 575 miles.
To find how far west the plane went, we need to calculate the westward component of the distance traveled. To do this, we can use the trigonometric relationship between the angle and the components of the velocity.
The westward component can be found using the formula:
Westward Distance = Distance × cos(angle)
In this case, the angle is 60 degrees north of west. So we can calculate:
Westward Distance = 575 miles × cos(60 degrees)
Using the cosine of 60 degrees (which is 0.5):
Westward Distance = 575 miles × 0.5 = 287.5 miles
Therefore, the plane traveled 287.5 miles west.
To find how far north the plane went, we need to calculate the northward component of the distance traveled. We can use the same trigonometric relationship, but this time, we are interested in the northward component:
Northward Distance = Distance × sin(angle)
In this case, the angle is 60 degrees north of west. So we can calculate:
Northward Distance = 575 miles × sin(60 degrees)
Using the sine of 60 degrees (which is √3/2 ≈ 0.866):
Northward Distance = 575 miles × 0.866 ≈ 498.55 miles
Therefore, the plane traveled approximately 498.55 miles north.
To find how fast the plane went west, we can use the westward velocity component. This can be calculated by dividing the westward distance traveled by the time taken:
Westward Speed = Westward Distance / Time
Given that the westward distance traveled is 287.5 miles and the time taken is 2.5 hours, we can calculate:
Westward Speed = 287.5 miles / 2.5 hours = 115 mph
Therefore, the plane was traveling at a speed of 115 mph west.
To find the distance traveled by the plane, you can use the formula:
Distance = Speed × Time
Given that the plane is flying at a speed of 230 mph for 2.5 hours, you can calculate the distance traveled by multiplying the speed by the time:
Distance = 230 mph × 2.5 hours = 575 miles
Therefore, the plane traveled 575 miles.
To find how far west the plane went, you can use the concept of vector components. The angle of 60 degrees north of west indicates that the plane is traveling in a direction that is 60 degrees counterclockwise from the west.
To determine the westward component of the plane's velocity, you can calculate:
Westward component = Speed × cos(angle)
In this case, the angle is 60 degrees. Using the cosine of 60 degrees (which is 0.5), you can find:
Westward component = 230 mph × 0.5 = 115 miles per hour (mph)
So, the plane traveled 115 miles west.
To find how far north the plane went, you can use the same concept of vector components. The angle of 60 degrees north of west indicates that the plane's motion has a northward component.
To determine the northward component of the plane's velocity, you can calculate:
Northward component = Speed × sin(angle)
In this case, the angle is 60 degrees. Using the sine of 60 degrees (√3/2), you can find:
Northward component = 230 mph × (√3/2) ≈ 199.36 miles per hour (mph)
So, the plane traveled approximately 199.36 miles north.
To find how fast the plane was going west, you can use the westward component of the velocity, which is 115 mph.