Physics · Kinematics · chapter 3 of 14

Class 11 Physics Chapter 3: Motion in a Plane case study question with answers

One case-based question of the kind CBSE-pattern school exams ask: a passage and a table, then 3 parts worth 4 marks in all, with the answer and the marking scheme for each. Written from the NCERT chapter.

Case study · 4 marks
At a science club in Kochi, Kavya uses a spring launcher that fires a small ball from floor level at 20 m s⁻¹ at any angle she chooses. She measures where the ball lands for five angles and records the ranges in the table. Air resistance is negligible and g = 10 m s⁻². She notices that two different angles often send the ball to the same spot, and wonders what else is the same for such a pair of throws.
angle of projection15°30°45°60°75°
range (m)20.034.640.034.620.0
Part 1 · 1 mark
The maximum height reached by the ball in the 30° throw is
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Answer: (b) 5 m

hm = (v₀ sin θ₀)²/2g = (20 × 0.5)²/20 = 5 m. 15 m is the height for the 60° throw.

Part 2 · 1 mark
The time of flight in the 60° throw is about
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Answer: (d) 3.46 s

Tf = 2v₀ sin θ₀/g = 2 × 20 × (√3/2)/10 = 2√3 ≈ 3.46 s. 1.73 s is the time to the top only.

Part 3 · 2 marks
Kavya says the 30° and 60° throws are 'the same throw'. Name the quantity that is the same for both and two quantities that differ, with their values.
Answer and marking scheme

Same: the range, 34.6 m, since sin 60° = sin 120°. Different: the maximum height, 5 m at 30° and 15 m at 60°; the time of flight, 2 × 20 × 0.5/10 = 2 s at 30° and 3.46 s at 60°.

  • range 34.6 m the same for both (1)
  • heights 5 m and 15 m, or times 2 s and 3.46 s, as the differences (1)
Or
Kavya lowers the launch speed to 10 m s⁻¹ and fires at 45°. Using the table and the dependence of range on speed, find the new range, and find how the maximum height changes from its value at 20 m s⁻¹.
Answer and marking scheme

R ∝ v₀²: halving the speed divides the range by 4, so 40.0/4 = 10 m. hm ∝ v₀² too: at 20 m s⁻¹ and 45°, hm = (20 × 0.707)²/20 = 10 m, so it falls to 10/4 = 2.5 m.

  • range ∝ v₀², new range 10 m (1)
  • maximum height falls by a factor 4, from 10 m to 2.5 m (1)
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