Two athletes jump straight up. John has twice the initial speed of Harry. Compared to Harry, John stays in the air

A) 0.50 times as long.

B) 1.41 times as long.

C) twice as long.

D) three times as long.

E) four times as long.

Question

Two athletes jump straight up. John has twice the initial speed of Harry. Compared to Harry, John stays in the air

A) 0.50 times as long.

B) 1.41 times as long.

C) twice as long.

D) three times as long.

E) four times as long.

BlackTom AI · Accepted Answer

Consider the scenario: two athletes launch straight upward from the same ground level, with John’s initial speed being twice Harry’s. For vertical projection under constant gravity, the total time in the air is t = 2 v0 / g, where v0 is the initial vertical speed. Since both launches are straight up, their vertical components equal their initial speeds, and gravity g is the same for both.

Option A: 0.50 times as long. This would imply John’s time is half Harry’s time. But because John’s initial speed is twice Harry’s, his total air time should be longer, not shorter. This option contradicts the direct proportionality t ∝ v0 for vertical throws.

Option B: 1.41 times as long. The factor 1.41 resembles sqrt(2), which would arise in a scenario with a 45-degree launch or some vector decomposition, not in a pure vertical throw with doubled speed. This is not applicable here.

Option C: twice as long. This aligns with the formula t = 2 v0 / g. If v0_J = 2 v0_H, then t_J = 2(2 v0_H)/g = 4 v0_H / g, while t_H = 2 v0_H / g, giving t_J / t_H = 2. Therefore John stays in the air twice as long as Harry.

Option D: three times as long. There is no basis for a factor of three from the straightforward proportionality t ∝ v0 in a vertical launch with the same g; this would require a different relationship or extra factors, which aren’t present here.

Option E: four times as long. While the ratio of speeds is 2:1, the time ratio is 2:1, not 4:1, because time scales linearly with initial speed, not with the square of it or other factors in this simple vertical motion scenario. This overstates the effect.

In summary, only Option C correctly reflects the direct proportionality between initial speed and air time for vertical launches with the same gravity, given John’s speed is twice Harry’s. The other options misapply proportionality, invoke irrelevant geometric factors, or assume incorrect scaling relationships.

2025 Fall PHYS 2205 TR 11:00 - 12:15 _ 89122 2205 Final Exam

Two athletes jump straight up. John has twice the initial speed of Harry. Compared to Harry, John stays in the air A) 0.50 times as long. B) 1.41 times as long. C) twice as long. D) three times as long. E) four times as long.

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