a person walks due east for 10 meters and the due north for 10 meters. what is the total distance?
b). what is the average speed of a car that travels 30 meters in 10 seconds, then another 50 meters in 30 seconds.
Thank you for answering.
Distance = total of distances
=10+10=20 m.
average speed
= total distance / total time
= (30+50)/(10+30) m/s
= ?
To find the total distance that a person travels, we can use the Pythagorean theorem. The person walks 10 meters due east and then 10 meters due north, forming a right triangle. The hypotenuse of this triangle will be the total distance traveled. Here's how you can calculate it:
1. Calculate the length of each side of the right triangle:
- The length of the eastward side is 10 meters.
- The length of the northward side is also 10 meters.
2. Use the Pythagorean theorem to find the length of the hypotenuse (total distance):
- The theorem states that the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).
- So, c^2 = a^2 + b^2
- In this case, c^2 = 10^2 + 10^2 = 100 + 100 = 200.
- Taking the square root of both sides, we find that c = sqrt(200) ≈ 14.14 meters.
Therefore, the total distance traveled by the person is approximately 14.14 meters.
Moving on to the second question:
To find the average speed of a car, we need to divide the total distance traveled by the total time taken. Here's how you can calculate it:
1. Calculate the total distance traveled by the car:
- The car travels 30 meters in the first 10 seconds.
- Then, it travels another 50 meters.
- So, the total distance traveled is 30 meters + 50 meters = 80 meters.
2. Calculate the total time taken by the car:
- The car takes 10 seconds to travel the first 30 meters.
- Then, it takes another 30 seconds to travel the next 50 meters.
- So, the total time taken is 10 seconds + 30 seconds = 40 seconds.
3. Calculate the average speed:
- Average speed is distance divided by time.
- In this case, average speed = total distance / total time = 80 meters / 40 seconds = 2 meters per second.
Therefore, the average speed of the car is 2 meters per second.