Trevo is bouncing back and forth. To create this animation, the animator used a reference sketch to mark each position of Trevo during the bouncing. Which option correctly represents the positions of Trevo in animator's reference sketch?

Question

Coloured strips are printed on a transparent sheet as shown below. The bottom half of this sheet is folded backwards along the PQ axis to form a semi-circle. Which of the option(s) will be a part of the resultant semi-circle?

Answer 1

Think of Trevo's bounce the same way a swing moves, it slows almost to a stop at the highest point of each arc and speeds up as it passes through the bottom.

If the animator marks Trevo's position at equal ticks of time, the marks will crowd together wherever Trevo is moving slowly, near the top of each side of the bounce, and spread apart wherever Trevo is moving fastest, through the middle.

Option C is the only sketch that shows this crowding at both ends and this wider spacing through the middle of the arc.

So Option C is the correct reference sketch for the bounce.

Answer 2

A different way to check this is to divide the arc into equal physical segments rather than equal time slices, and count how many marks fall inside each segment.

Option A: would show fewer marks per segment near the ends of the arc and more marks per segment in the middle, which does not match a bounce, where the object lingers near the extremes.
Option B: spreads exactly one mark per equal segment everywhere, again describing constant speed rather than a bounce.
Option C: shows several marks packed into the segments nearest each extreme, meaning Trevo takes many equal time-steps to cross that short stretch, and only a few marks across the wide middle segment, meaning Trevo crosses that stretch quickly; this matches an object slowing near the top of a bounce and speeding through the bottom.
Option D: shows the reverse pattern to what a bounce needs, with marks packed into the middle segment instead of the end segments.

Only Option C packs marks into the end segments and spreads them thinly across the middle, matching how a bouncing object actually spends its time.

Therefore, the correct answer is Option C.

Answer 3

A different way to check this is to divide the arc into equal physical segments rather than equal time slices, and count how many marks fall inside each segment.

Option A: would show fewer marks per segment near the ends of the arc and more marks per segment in the middle, which does not match a bounce, where the object lingers near the extremes.
Option B: spreads exactly one mark per equal segment everywhere, again describing constant speed rather than a bounce.
Option C: shows several marks packed into the segments nearest each extreme, meaning Trevo takes many equal time-steps to cross that short stretch, and only a few marks across the wide middle segment, meaning Trevo crosses that stretch quickly; this matches an object slowing near the top of a bounce and speeding through the bottom.
Option D: shows the reverse pattern to what a bounce needs, with marks packed into the middle segment instead of the end segments.

Only Option C packs marks into the end segments and spreads them thinly across the middle, matching how a bouncing object actually spends its time.

Therefore, the correct answer is Option C.