Roll a toy car down a ramp from five heights. Measure how far it rolls, average your trials, and find out if rollout = k × height.
Two quantities are proportional when one is always the same number times the other: y = kx
Here x is the ramp height and y is how far the car rolls. k is the constant of proportionality: how many cm the car rolls for each 1 cm of height. You'll find k in a table (y ÷ x), see it on a graph (a straight line through (0, 0) and (1, k)), and use it in an equation to predict.
Track: one straight 120 cm piece. The top end rests on books; the bottom end touches the zero line. Height = floor to the top end.
Your data saves to your account as you go, and each mission earns XP and Gold once. Lost your lab sheet? Open this lab again to see every number.
Every car is a little different, and so is every floor. Once you find k for one car, try another and compare.
Average = add the 3 trials, divide by 3, round to the tenth. Ratio = average ÷ height, round to the hundredth. In a proportional relationship every ratio y ÷ x is the same number, k. Real measurements wobble a little, so look for ratios that are close.
Each average you get right lands on the graph. A proportional relationship graphs as a straight line through the origin (0, 0). Find k to draw y = kx: the line also passes through (1, k), so k is how steep it is.
The car's energy comes from its starting height. Floor friction takes that energy away a little at a time as the car rolls. Twice the height gives twice the energy, so the car rolls about twice as far. That makes rollout = k × height, and k depends on the car and the floor.
It's only approximately proportional. Every run loses a small fixed amount of energy on the track and at the bump at the bottom. That small loss matters most for low ramps, so the 10 cm ratio usually comes out a bit lower than the rest.
Find k in Mission 2 to unlock.