A plane flies 230 mph at 60 degrees north of west for 2.5 hours. Answer the following questions.
A. How far did it travel total?
B. How far west did it go?
C. How far north did it go?
D. How fast did it go west?
I don't know how to do this problem :(
No problem! I can guide you through it step by step.
Step 1: Draw a diagram to visualize the problem. On a piece of paper, draw a coordinate system with an arrow pointing west (left) labeled as "W" and another arrow pointing north labeled as "N".
Step 2: Identify the given information:
- Speed of the plane: 230 mph
- Angle of the plane's path: 60 degrees north of west
- Time traveled: 2.5 hours
Step 3: Breaking down the given information:
- The plane is flying at a speed of 230 mph. This represents the magnitude or the total distance traveled by the plane.
- The angle given (60 degrees north of west) tells us the direction of the plane's path.
Step 4: Calculate the horizontal and vertical components of the plane's motion. We can use trigonometry to find these components.
Step 4a: Horizontal Component (westward direction)
Use the cosine function to find the horizontal component since the angle given is north of west.
cos(60°) = adjacent / hypotenuse
adjacent = cos(60°) * 230 mph
adjacent = 115 mph
Step 4b: Vertical Component (northward direction)
Use the sine function to find the vertical component.
sin(60°) = opposite / hypotenuse
opposite = sin(60°) * 230 mph
opposite = 199.9 mph (rounding to the nearest hundredth)
Step 5: Calculate the answers to the questions.
A. Total distance traveled:
To find the total distance traveled, we can use the Pythagorean theorem.
Distance = √(horizontal component^2 + vertical component^2)
Distance = √(115^2 + 199.9^2)
Distance ≈ 232.37 miles (rounding to the nearest hundredth)
B. Distance traveled west:
The distance traveled west is equal to the horizontal component, which is 115 mph.
C. Distance traveled north:
The distance traveled north is equal to the vertical component, which is approximately 199.9 mph.
D. Speed west:
The speed west is the same as the horizontal component, which is 115 mph.
So, the answers are:
A. The plane traveled approximately 232.37 miles in total.
B. The plane traveled 115 miles west.
C. The plane traveled approximately 199.9 miles north.
D. The plane traveled at a speed of 115 mph westward.
If you have any more questions, feel free to ask!
No worries! I can help you solve this problem step by step.
First, let's break down the given information. The plane flies at a speed of 230 mph (miles per hour) and at an angle of 60 degrees north of west for a duration of 2.5 hours.
A. To find out how far the plane traveled in total, we can use the formula:
Distance = Speed × Time
So, in this case, Distance = 230 mph × 2.5 hours. By multiplying these two values together, you will find the total distance traveled by the plane.
B. To determine how far west the plane went, we need to use some trigonometry. Since the plane is flying at an angle of 60 degrees north of west, we can split this into two components: the westward component and the northward component. To find the westward component, we can calculate the cosine of the given angle and multiply it by the total distance traveled.
Westward Distance = Distance × cos(60 degrees)
C. Similarly, to find out how far north the plane went, we need to calculate the sine of the given angle and multiply it by the total distance traveled.
Northward Distance = Distance × sin(60 degrees)
D. The speed at which the plane traveled westward can be determined by dividing the westward distance by the time taken.
Speed Westward = Westward Distance / Time
Now that you know the step-by-step process, you can use a calculator or appropriate formulas to find the answers to these questions.