Mathematical routines (MR)
Will the ball clear the wall?
- Unit 1
- 10 points
- About 22 minutes
You can use a calculator on this question, just like on exam day.
A multipart problem where you use math to analyze a physical situation. You draw or sketch a representation such as a free-body diagram or a graph, derive an equation using letters, calculate a numerical answer with units, and then make a claim or prediction and justify it with physics reasoning. On the exam: Question 1 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 20–25 minutes.
The question
A ball is launched from ground level with speed v₀ = 14 m/s at an angle θ = 30° above the horizontal, directly toward a vertical wall that is D = 12 m away and 2.5 m tall. Air resistance is negligible. Use g = 9.8 m/s² (answers that use g = 10 m/s² are also accepted).
Suggested time: 22 minutes
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Part (a)
2 pointsDescribe a diagram of the ball at the highest point of its path that shows (i) its velocity vector and (ii) its acceleration vector. Give the magnitude and direction of each.
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Part (b)
3 pointsDerive an expression for the height y of the ball at the moment it reaches the wall, in terms of v₀, θ, D, and g, as appropriate.
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Part (c)
3 pointsCalculate (i) the height of the ball when it reaches the wall and (ii) the vertical component of its velocity at that moment, including its direction. Does the ball clear the wall?
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Part (d)
2 pointsA student says that launching the ball at 45° with the same speed will make it clear the wall, "because 45° gives the maximum range." Evaluate the student's reasoning, and determine whether the ball launched at 45° clears the wall.
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