Question

rolling a car down a ramp

	height (centimeters)	distance rolled (centimeters)
test 1	5 cm	16 cm
test 2	?	22 cm
test 3	15 cm	27 cm

options: 2 cm, 30 cm, 10 cm, 25 cm

Explanation:

Step1: Analyze the trend

We can see that as the height increases, the distance rolled also increases. Let's check the relationship between height and distance. From Test 1 (5 cm height, 16 cm distance) to Test 3 (15 cm height, 27 cm distance), the height increases by 10 cm (15 - 5) and the distance increases by 11 cm (27 - 16). Now, Test 2 has a distance of 22 cm, which is 6 cm more than Test 1's distance (22 - 16 = 6). So we can assume a linear relationship (approximate) and find the corresponding height increase.

Step2: Calculate the height for Test 2

The increase in distance from Test 1 to Test 2 is 22 - 16 = 6 cm. The increase in height from Test 1 to Test 3 is 15 - 5 = 10 cm, and the increase in distance is 27 - 16 = 11 cm. But a simpler way is to see the midpoint or the linear approximation. Let's list the heights and distances:

• Height: 5,?, 15
• Distance: 16, 22, 27

The distance increases from 16 to 22 (increase of 6) and then to 27 (increase of 5). The height increases from 5 to? and then to 15. Let's assume a linear relationship between height (h) and distance (d). The slope (m) between Test 1 and Test 3 is $\frac{15 - 5}{27 - 16}=\frac{10}{11}\approx0.909$. Now, for Test 2, the distance is 22, so the change in distance from Test 1 is 22 - 16 = 6. So the change in height should be $6\times\frac{10}{11}\approx5.45$, but that's not exact. Wait, maybe it's a simple pattern. Let's check the differences:

From Test 1 to Test 2: distance increases by 6 (22 - 16), height should increase by some amount. From Test 2 to Test 3: distance increases by 5 (27 - 22), height increases by 15 -?

Wait, maybe the height values are 5, 10, 15 (increasing by 5 each time) and distance: 16, 22, 27 (increasing by 6 then 5? No, 16 to 22 is +6, 22 to 27 is +5. But if height is 5, 10, 15 (step of 5), then distance would be 16, 22, 27. Let's check: 5 cm height, 16 cm distance; 10 cm height, 22 cm distance (16 + 6); 15 cm height, 27 cm distance (22 + 5). That fits. So the missing height is 10 cm.

Answer:

10 cm