Aim for FivePhysics 1

Qualitative/quantitative translation (QQT)

Ball launched from a moving cart

  • Unit 1
  • 8 points
  • About 18 minutes

You can use a calculator on this question, just like on exam day.

A shorter multipart problem that connects reasoning in words with an equation. You make and justify a claim without equations, derive an equation from a physics principle, and then explain whether the two agree or use them to predict what happens in a changed situation. On the exam: Question 4 of 4. Section II has 4 questions in 95 minutes (50% of the exam score), one of each type in this order; calculator allowed. The CED suggests 15–20 minutes.

The question

A cart moves to the right at a constant speed v = 2.0 m/s along a long, level track. A spring launcher mounted on the cart fires a small ball straight up relative to the cart with speed u = 4.9 m/s. Air resistance is negligible, and the ball is caught at the same height from which it was launched. Use g = 9.8 m/s² (answers that use g = 10 m/s² are also accepted).

Suggested time: 18 minutes

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Part (a)

3 points

(i) Does the ball land in front of the launcher, behind it, or back in the launcher? (ii) Describe the shape of the ball's path as seen by an observer riding on the cart and by an observer standing beside the track. Justify your answers. Do not use equations in this part; reason in words.

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Part (b)

3 points

Derive an expression for the horizontal distance d the cart travels, relative to the ground, while the ball is in the air, in terms of u, v, and g. Then calculate d.

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Part (c)

2 points

Now suppose the cart is speeding up with a constant acceleration of 0.50 m/s² to the right during the ball's flight. The ball is launched the same way at the moment the cart's speed is 2.0 m/s. Use your reasoning from part (a) and your work from part (b) to predict where the ball lands relative to the launcher.

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