Question

rolling a car down a ramp
height (centimeters) | distance rolled (centimeters)
test 1 | 5 cm | 16 cm
test 2 | 10 cm | 22 cm
test 3 | 15 cm | ?
options: 18 cm, 10 cm, 27 cm, 5 cm

Explanation:

Step1: Analyze the pattern

From Test 1 to Test 2, height increases by \(10 - 5 = 5\) cm, and distance rolled increases by \(22 - 16 = 6\) cm.

Step2: Predict for Test 3

For Test 3, height increases by \(15 - 10 = 5\) cm from Test 2. So distance rolled should increase by 6 cm from Test 2's distance. So \(22 + 6 = 28\)? Wait, but the options have 27. Wait, maybe the pattern is linear. Let's check the slope. From (5,16) to (10,22), slope is \(\frac{22 - 16}{10 - 5}=\frac{6}{5}=1.2\). So for x=15, y=16 + 1.2*(15 - 5)=16 + 12=28. But the options have 27. Wait, maybe the increase is 5 to 10 (height +5) distance +6 (16 to 22), then 10 to 15 (height +5) distance +5? No, 22 +5=27. So maybe the pattern is that each 5 cm height increase, distance increases by 6, then 5? Wait, the options have 27, which is 22 +5? Wait, maybe my initial analysis is wrong. Let's see the options. The options are 18,10,27,5. 27 is the only one that makes sense as a reasonable increase. So the answer should be 27 cm.

Answer:

27 cm (the option with "27 cm")