Question

A long, straight conveyor belt at a sushi restaurant carries sushi past customers with a constant velocity. If the sushi roll you want is 4.30 m to the right of you 11.0 s after exiting the little door at the beginning of the conveyor belt, and it is still 2.10 m to the right of you 10.0 s later, how far is the little door to the right of you?

Answer 1

To solve this problem, we can use the equation:

distance = velocity × time

Let's assume that the velocity of the conveyor belt is v, and the distance between the little door and the sushi roll is d.

According to the information given, the sushi roll is 4.30 m to the right of you 11.0 s after exiting the little door. We can write this as:

4.30 m = v × 11.0 s

Similarly, the sushi roll is still 2.10 m to the right of you 10.0 s later:

2.10 m = v × 10.0 s

Now, we can solve these two equations simultaneously to find the velocity of the conveyor belt. Dividing the second equation by the first equation, we get:

2.10 m / 4.30 m = (v × 10.0 s) / (v × 11.0 s)

Simplifying, we find:

0.4884 ≈ 0.9091

Now, we can use either equation to find the value of v. Let's use the first equation:

4.30 m = v × 11.0 s

Dividing both sides by 11.0 s:

v ≈ 4.30 m / 11.0 s

v ≈ 0.3909 m/s

Now that we know the velocity of the conveyor belt, we can calculate the distance between the little door and you. Using the second equation:

2.10 m = v × 10.0 s

Substituting the value of v:

2.10 m = 0.3909 m/s × 10.0 s

2.10 m = 3.909 m

Therefore, the little door is approximately 3.909 meters to the right of you.