ACT Science: Data Representation (Drill 4) is a Science practice drill covering Data Representation. It contains 5 original questions created by Brian Stewart, a Barron's test prep author with over 20 years of tutoring experience.
ACT Data Representation questions ask you to read experimental data carefully and draw accurate conclusions. This drill uses figures showing horizontal range and maximum height versus launch angle for a projectile, requiring trend analysis, data comparison, and prediction tasks.
Figures 1 and 2
Physics students launched a steel ball using a spring-loaded launcher positioned at ground level. The launch speed was held constant at 20 m/s for all trials. In a series of trials, the launch angle was varied from 10° to 80° in increments of 10°, with an additional trial at 45°. For each angle, the students recorded the horizontal range (the horizontal distance from the launch point to where the ball landed) and the maximum height reached during flight. Air resistance was considered negligible. Results are shown in Figures 1 and 2.
Figure 1. Horizontal Range vs. Launch Angle
Range (m)
Launch Angle (°)
0
10
20
30
40
50
10°
20°
30°
40°
45°
50°
60°
70°
80°
Figure 2. Maximum Height vs. Launch Angle
Max Height (m)
Launch Angle (°)
0
5
10
15
20
25
10°
20°
30°
40°
45°
50°
60°
70°
80°
Question 1. According to Figure 1, at which launch angle was the horizontal range the greatest?
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A) 30°
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B) 40°
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C) 45° ✓
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D) 60°
Explanation: In Figure 1, the range curve peaks at 45°, where the range reaches approximately 40.8 m, the highest point on the graph. The curve is symmetric around 45°, so angles equally far from 45° produce equal ranges. The maximum occurs at 45° because range = v²sin(2θ)/g, which is maximized when 2θ = 90°, i.e., θ = 45°.
Figure 2
Physics students launched a steel ball using a spring-loaded launcher positioned at ground level. The launch speed was held constant at 20 m/s for all trials. In a series of trials, the launch angle was varied from 10° to 80° in increments of 10°, with an additional trial at 45°. For each angle, the students recorded the horizontal range (the horizontal distance from the launch point to where the ball landed) and the maximum height reached during flight. Air resistance was considered negligible. Results are shown in Figures 1 and 2.
Figure 2. Maximum Height vs. Launch Angle
Max Height (m)
Launch Angle (°)
0
5
10
15
20
25
10°
20°
30°
40°
45°
50°
60°
70°
80°
Question 2. According to Figure 2, as the launch angle increased from 10° to 80°, the maximum height:
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A) increased then decreased, peaking at 45°
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B) decreased steadily
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C) increased steadily ✓
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D) remained constant regardless of angle
Explanation: Figure 2 shows maximum height increasing continuously from about 0.6 m at 10° to about 19.8 m at 80°, a steady monotonic increase with no peak or reversal. Maximum height = v²sin²(θ)/(2g). As θ increases from 10° to 80°, sin(θ) increases throughout, so height increases continuously. Unlike range, height has no symmetric peak, the higher you aim, the higher you go (though range eventually decreases).
Figure 1
Physics students launched a steel ball using a spring-loaded launcher positioned at ground level. The launch speed was held constant at 20 m/s for all trials. In a series of trials, the launch angle was varied from 10° to 80° in increments of 10°, with an additional trial at 45°. For each angle, the students recorded the horizontal range (the horizontal distance from the launch point to where the ball landed) and the maximum height reached during flight. Air resistance was considered negligible. Results are shown in Figures 1 and 2.
Figure 1. Horizontal Range vs. Launch Angle
Range (m)
Launch Angle (°)
0
10
20
30
40
50
10°
20°
30°
40°
45°
50°
60°
70°
80°
Question 3. Based on Figure 1, which two launch angles produced the same horizontal range?
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A) 10° and 45°
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B) 30° and 60°
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C) 40° and 50° in the experiment described
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D) Both B and C ✓
Explanation: Figure 1 shows a symmetric curve peaking at 45°. Any two angles equally spaced around 45° produce identical ranges: 30° and 60° (each 15° from 45°) both yield approximately 35.4 m; 40° and 50° (each 5° from 45°) both yield approximately 40.2 m. Both pairs satisfy the condition, making D correct. This symmetry comes from R = v²sin(2θ)/g, since sin(2θ) = sin(180°−2θ), complementary angle pairs always give equal ranges.
Figures 1 and 2
Physics students launched a steel ball using a spring-loaded launcher positioned at ground level. The launch speed was held constant at 20 m/s for all trials. In a series of trials, the launch angle was varied from 10° to 80° in increments of 10°, with an additional trial at 45°. For each angle, the students recorded the horizontal range (the horizontal distance from the launch point to where the ball landed) and the maximum height reached during flight. Air resistance was considered negligible. Results are shown in Figures 1 and 2.
Figure 1. Horizontal Range vs. Launch Angle
Range (m)
Launch Angle (°)
0
10
20
30
40
50
10°
20°
30°
40°
45°
50°
60°
70°
80°
Figure 2. Maximum Height vs. Launch Angle
Max Height (m)
Launch Angle (°)
0
5
10
15
20
25
10°
20°
30°
40°
45°
50°
60°
70°
80°
Question 4. A student wants to maximize the height reached by the ball while keeping the horizontal range above 20 m. Based on Figures 1 and 2, which launch angle best satisfies both conditions?
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A) 30°
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B) 45°
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C) 60°
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D) 70° ✓
Explanation: From Figure 1, 80° produces a range of only about 14 m, below the 20 m threshold, so it is eliminated. Among the remaining options, Figure 2 shows height increases with angle, so 70° (height ≈ 18.0 m, range ≈ 26.2 m) produces greater height than 60° (height ≈ 15.3 m, range ≈ 35.4 m), 45° (height ≈ 10.2 m), or 30° (height ≈ 5.1 m), while all four still satisfy the range requirement. 70° is the correct answer.
Figure 1
Physics students launched a steel ball using a spring-loaded launcher positioned at ground level. The launch speed was held constant at 20 m/s for all trials. In a series of trials, the launch angle was varied from 10° to 80° in increments of 10°, with an additional trial at 45°. For each angle, the students recorded the horizontal range (the horizontal distance from the launch point to where the ball landed) and the maximum height reached during flight. Air resistance was considered negligible. Results are shown in Figures 1 and 2.
Figure 1. Horizontal Range vs. Launch Angle
Range (m)
Launch Angle (°)
0
10
20
30
40
50
10°
20°
30°
40°
45°
50°
60°
70°
80°
Question 5. If the students repeated the experiment with a launch speed of 10 m/s instead of 20 m/s, which of the following would most likely be true about the shape of the range curve in Figure 1?
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A) The curve would peak at a different angle, shifted toward 60° for the experiment described
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B) The curve would have the same shape but all range values would be lower ✓
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C) The curve would be inverted, with minimum range at 45°
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D) The curve would become a flat horizontal line
Explanation: Range = v²sin(2θ)/g. Halving v from 20 m/s to 10 m/s reduces v² by a factor of 4, so all range values drop to one-quarter of their original values (e.g., the 45° peak drops from ~40.8 m to ~10.2 m). However, the angle dependence, sin(2θ), is unchanged, so the curve still peaks at 45° with the same symmetric shape. Only the scale changes, not the shape or peak angle. The optimal launch angle for maximum range is always 45° regardless of launch speed (ignoring air resistance).