Why did we assume it to be 45 degrees?

In summary: No problem! In summary, for a 6 minute trip where a motorist drives south at 20 m/s for 3 min, turns west and travels west at 25 m/s for 2 min, and finally travels northwest at 30 m/s for 1 min, the net vector displacement is 1273 m west and 1273 m north. This is because the angle between west and north is 45 degrees, as the problem states the motorist is traveling northwest. So, the 90 degree angle is divided in half to find the angle of the northwest direction. The typo in the calculation of the second distance is corrected to 2 min.

Homework Statement

a motorist drives south at 20 m/s for 3 min, then turns west and travels west at 25m/s for 2 min, and finally travels n/w at 30 m/s for 1 min. for this 6 minute trip, find the net vector displacement

The Attempt at a Solution

distance 1: 20m/s * 3min * 60s/min = 3600m south
distance 2: 25m/s * 2.6min * 60s/min = 3900m west
distance 3: 30m/s * 1min * 60s/min * cos45 = 1273m west
... 30m/s * 1min * 60s/min * sin45 = 1273m north

My real problem is why we assumed the angle is 45 degrees? Why did we dissect the 90 degree angle in half for the north west if it doesn't tell us in the problem?

My real problem is why we assumed the angle is 45 degrees? Why did we dissect the 90 degree angle in half for the north west if it doesn't tell us in the problem?
It says that it travels n/w = northwest, which means half-way between North and West. That's where the 45 degrees comes in.

doc al said:
it says that it travels n/w = northwest, which means half-way between north and west. That's where the 45 degrees comes in.

thank you!

In the problem statement it says "travels west at 25m/s for 2 min" yet in your attempt at a solution you change it to 2.6 min. Why?

skeptic2 said:
In the problem statement it says "travels west at 25m/s for 2 min" yet in your attempt at a solution you change it to 2.6 min. Why?

just a silly typo sorry

1. Why is 45 degrees considered a standard angle in geometry?

45 degrees is considered a standard angle in geometry because it is the angle formed when a straight line is cut in half, creating two equal angles of 45 degrees each. This makes it a convenient and easily divisible angle for mathematical calculations.

2. What is the significance of 45 degrees in trigonometry?

In trigonometry, 45 degrees is significant because it is one of the special angles that has a simple and exact value for its sine, cosine, and tangent ratios. The sine and cosine of 45 degrees are both equal to √2/2, while the tangent is equal to 1.

3. How is 45 degrees related to right angles and the Pythagorean theorem?

45 degrees is exactly half of a right angle, which measures 90 degrees. This means that a right triangle with one 45 degree angle will have the other two angles measuring 45 degrees and 90 degrees. Additionally, in a right triangle with sides of equal length (an isosceles right triangle), the length of the hypotenuse (the side opposite the right angle) can be calculated using the Pythagorean theorem as √2 times the length of either of the other two sides.

4. Why is 45 degrees often used in construction and engineering?

In construction and engineering, 45 degrees is often used as a standard angle for creating diagonal or diagonal supports, as it provides a good balance between strength and stability. Additionally, 45 degree angles are commonly used in miter joints, where two pieces of material are joined at a 45 degree angle to create a 90 degree corner.

5. Is there a historical or cultural significance to the 45 degree angle?

There is no specific historical or cultural significance to the 45 degree angle. However, it has been used in various cultures and traditions as a symbol for balance, harmony, and stability. In Chinese culture, the number 45 is considered lucky and represents good fortune and success.

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