Question

step 8: observe how changes in the speed of beanbag height

calculate the average maximum height for all three trials when the speed of the bottle is 2 m/s, 3 m/s, 4 m/s, 5 m/s, and 6 m/s.
record your calculations in table b of your student guide.

when the speed of the
maximum height of the
1.82

when the speed of the
maximum height of the
1.86

when the speed of the
maximum height of the
1.89

when the speed of the
maximum height of the
1.92

when the speed of the bottle is 6 m/s, the average maximum height of the beanbag is
m.

Explanation:

Step1: Identify the pattern

Looking at the given heights: 1.82, 1.86, 1.89, 1.92. Let's check the differences. From 1.82 to 1.86: +0.04; 1.86 to 1.89: +0.03; 1.89 to 1.92: +0.03? Wait, maybe it's a linear increase or we can assume the next value. Wait, maybe the values are for speeds 2,3,4,5 m/s and we need 6 m/s. Wait, the previous differences: 1.82 (2m/s), 1.86 (3m/s: +0.04), 1.89 (4m/s: +0.03), 1.92 (5m/s: +0.03). Wait, maybe the next one (6m/s) would be 1.92 + 0.03 = 1.95? Wait, no, maybe I misread. Wait, the problem says "calculate the average maximum height for all three trials" but the given numbers are maybe the averages for 2,3,4,5 m/s? Wait, the last one is for 6 m/s. Wait, maybe the sequence is increasing by a certain amount. Let's check the differences between consecutive terms:

1.86 - 1.82 = 0.04

1.89 - 1.86 = 0.03

1.92 - 1.89 = 0.03

Wait, maybe the next difference is 0.03? So 1.92 + 0.03 = 1.95? Wait, but maybe it's a linear regression or just a pattern. Alternatively, maybe the numbers are 1.82 (2), 1.86 (3), 1.89 (4), 1.92 (5), so for 6, let's see the slope. From 2 to 5: 3 steps, height increases from 1.82 to 1.92, which is 0.1 over 3 steps, so per step (per m/s increase) is 0.1/3 ≈ 0.033. So from 5 to 6 (1 step), 1.92 + 0.033 ≈ 1.953, but maybe the intended pattern is adding 0.03 each time after the first. Wait, 1.82 (2), 1.86 (3: +0.04), 1.89 (4: +0.03), 1.92 (5: +0.03), so 6: +0.03 → 1.95. Alternatively, maybe the numbers are 1.82, 1.86, 1.89, 1.92, and the next is 1.95. Wait, but maybe I made a mistake. Wait, the problem is about calculating the average, but maybe the given numbers are the averages for each speed, and we need to find the next one. Wait, maybe the user expects a pattern. Let's check the differences again:

1.86 - 1.82 = 0.04

1.89 - 1.86 = 0.03

1.92 - 1.89 = 0.03

So the first increase is 0.04, then two increases of 0.03. So maybe the next is 0.03, so 1.92 + 0.03 = 1.95. So the average maximum height when speed is 6 m/s is 1.95 m.

Step2: Confirm the pattern

Assuming the pattern of increasing by 0.03 after the first increase of 0.04, the next value (for 6 m/s) is 1.92 + 0.03 = 1.95.

Answer:

1.95