Would someone like to help me with these questions?

Steps appreciated~

1. If the diameter of a monster truck tire is 3.5 m and it makes one rotation every 5 seconds, how far does the tire
roll in 1 minute?
--------------------------------------
2. At t=0 a car is due 2 km north of you heading west moving 13 km/s after 1.5s. What is the angle in radians between you and the car from where the car was at t=0?

a) 2.306 rads
b) 0.9475 rads
c) 2.936 rads
d) 1.468 rads
-------------------------------------

1) 23, sorry i don't know the other one :(

Please ignore all answers and posts of kk-gothgirl-kk.

1. pi*D*(60/5 revolutions) = 131.9 meters

2. Check your problem statement again. No car can travel 13 km/s. That is more like the velocity of a launched rocket. If you meant 13 m/s, the car would only move 19.5 m in 1.5 s, and the angular displacement would be smaller than any of your choices.

My guess is that you copied both the speed and time dimensions wrong.

Thanks Drwls!

For 1, I got the same answer however, the book says 263.89 m

okay , i must say i thought it said how many times does it turn. if it was what i thought it was then my answer would have been correct. it was not therefore it was wrong. i take responsibility. IT WAS JUST A FRIGGIN MISTAKE !!!!!!!!!!!!!!

I'd be happy to help you with these questions! Here are the steps to find the answers:

1. To calculate the distance the tire rolls in 1 minute, we need to find the distance it covers in one rotation, and then multiply it by the number of rotations in 1 minute.

Step 1: Calculate the circumference of the tire
- The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle.
- Since we have the diameter, which is twice the radius, we can divide it by 2 to get the radius.
- In this case, the radius is 3.5 m / 2 = 1.75 m.

Step 2: Calculate the distance covered in one rotation
- The distance covered in one rotation is equal to the circumference of the tire.
- From Step 1, we found that the circumference is 2πr, so for this tire, it is 2π(1.75) ≈ 11.0 m.

Step 3: Calculate the distance covered in 1 minute
- Since the tire makes one rotation every 5 seconds, there are 60/5 = 12 rotations in 1 minute.
- Finally, multiply the distance covered in one rotation (Step 2) by the number of rotations in 1 minute:
- Distance covered in 1 minute = 11.0 m/rotation * 12 rotations = 132.0 m.

Therefore, the tire rolls approximately 132.0 meters in 1 minute.

2. To find the angle in radians between you and the car from where the car was at t=0, we can use trigonometry.

Step 1: Draw a diagram
- Sketch a diagram representing the car and you. Mark the initial position of the car, and the line connecting you and the car as a vector.

Step 2: Calculate the distance covered by the car in 1.5 seconds
- Given that the car is moving at 13 km/s, after 1.5 seconds, it would have covered a distance of 13 km/s * 1.5 s = 19.5 km.

Step 3: Use trigonometry to find the angle in radians
- First, convert the distance covered by the car into meters (1 km = 1000 m).
- In this case, the distance covered by the car is 19.5 km * 1000 m/km = 19500 m.
- Now, consider the right triangle formed by the car's initial position, the car's final position, and you. The side representing the distance between the car's initial and final positions is the hypotenuse of the triangle.
- The angle between you and the car from where the car was at t=0 is the angle whose opposite side is the distance covered by the car, and whose adjacent side is the distance between you and the car at t=0.
- Use the tangent function to find the angle: tan(angle) = opposite/adjacent.
- In this case, tan(angle) = 19500 m/2000 m (2 km).
- Solve for the angle: angle = arctan(19500 m/2000 m) ≈ 1.468 radians.

Therefore, the angle in radians between you and the car from where the car was at t=0 is approximately 1.468 radians (option d).