Amy walks at an average speed of 1.75 m/s toward her airport gate. When she comes within 57.5 m of her gate, she gets onto and continues to walk on a people mover at the same rate. (A) If she arrives at the gate 15.3 seconds after getting on the people mover how fast was the moving relative to the ground? (B) What was the speed of the people mover?

A. d = V*T = 57.5 m

V*15.3 = 57.5
V = 3.76 m/s

B. V = Va + Vp = 3.76
1.75 + Vp = 3.76
Vp = 2.0 m/s

To solve this problem, we can use the concept of relative velocity.

(A) To find the speed of the people mover relative to the ground, we need to determine the difference between Amy's walking speed and her total speed on the people mover.

Let's first calculate the time it took for Amy to walk the distance of 57.5 m.

Using the formula distance = speed × time, we have:

57.5 m = 1.75 m/s × t1

Solving for t1:

t1 = 57.5 m / 1.75 m/s
≈ 32.86 seconds

Next, we can calculate the speed of the people mover relative to the ground:

Let v be the speed of the people mover relative to the ground.

On the people mover, Amy's speed (relative to the ground) is the sum of her walking speed and the speed of the people mover.

Since Amy spends 15.3 seconds on the people mover, the distance she covers on the people mover is:

Distance on people mover = (Amy's walking speed + v) × 15.3 seconds

This distance is equal to the remaining distance to the gate:

Distance on people mover = 57.5 m - (1.75 m/s × 15.3 s)

Setting these two distances equal and solving for v, we have:

(Amy's walking speed + v) × 15.3 seconds = 57.5 m - (1.75 m/s × 15.3 s)

(1.75 m/s + v) × 15.3 seconds = 57.5 m - 26.775 m

(1.75 m/s + v) × 15.3 seconds = 30.725 m

1.75 m/s + v = 30.725 m / 15.3 s

1.75 m/s + v ≈ 2.0098 m/s

v ≈ 2.0098 m/s - 1.75 m/s
≈ 0.2598 m/s

Therefore, the speed of the moving walkway relative to the ground (v) is approximately 0.2598 m/s.

(B) We have found the speed of the people mover relative to the ground. Now, let's determine the speed of the people mover itself.

The speed of the people mover itself is the relative speed between Amy on the people mover and Amy walking. As we've calculated in part (A), this relative speed is approximately 0.2598 m/s.

Hence, the speed of the people mover is approximately 0.2598 m/s.

To find the answer to both parts (A) and (B), we can use the concept of relative speeds.

Let's first analyze the situation. Amy walks at a constant speed of 1.75 m/s towards her airport gate. When she gets onto the people mover, her speed relative to the ground remains the same because she is on the moving platform. We need to find the speed of the people mover.

Let's assume the speed of the people mover is "v" m/s.

Part (A):
Amy arrives at the gate 15.3 seconds after getting on the people mover. Therefore, we need to find the speed of the people mover relative to the ground.

We know that Amy walks for a distance of 57.5 m before getting on the people mover. So, the time taken to cover this distance at a speed of 1.75 m/s is:
Time = Distance / Speed = 57.5 m / 1.75 m/s = 33 seconds

Amy walks for 33 seconds before getting on the people mover. After getting on the people mover, she arrives at the gate in an additional 15.3 seconds. So, the total time taken from the start to reaching the gate is:
Total Time = Time walked + Time on the people mover
Total Time = 33 seconds + 15.3 seconds = 48.3 seconds

Now, the total distance traveled by Amy is the sum of the distance she walked and the distance covered by the people mover:
Total Distance = Distance walked + Distance on the people mover
Total Distance = 57.5 m + Distance on the people mover

We can calculate the distance covered by the people mover using the formula: Distance = Speed × Time
Distance on the people mover = Speed of the people mover × Time on the people mover

Substituting the known values:
Total Distance = 57.5 m + (v m/s) × 15.3 s

Since the total distance traveled is the same regardless of whether Amy walks or is on the people mover, we can form the equation:
57.5 m + (v m/s) × 15.3 s = 1.75 m/s × 48.3 s

Solving this equation will give us the speed of the people mover relative to the ground (v).

Part (B):
Once we have found the speed of the people mover (v) in part (A), that will be the answer to part (B) as well.

To find the speed of the people mover, we substitute the calculated value of v into the equation we formed in part (A), and solve for v.

By following these steps, we can determine the speed of the people mover relative to the ground, which will be the answer to both parts (A) and (B).