Mechanics
⏱ ~3-min readAceMark Guide
What this topic is really about
The range of a projectile is identical for complementary angles of projection, such as 30 degrees and 60 degrees, because sin(2*theta) has the same value for both. Option C is incorrect because doubling the angle of projection does not double the range. Instead, the range remains exactly R due to this trigonometric symmetry.
The kinetic energy is calculated using the relation KE = p^2 / (2m), which yields 100 / 4 = 25 J. Option B is incorrect because 50 J is obtained if you neglect the factor of 2 in the denominator, using p^2/m instead. Option C incorrectly assumes kinetic energy equals the momentum squared.
See the mechanism
Using the third equation of motion, the maximum height is calculated as u^2 / (2g), which yields 20^2 / 20 = 20 meters. A diagram for this topic isn't available yet — the worked example below walks the same reasoning step by step.
An exam-style question, fully explained
A ball is thrown vertically upward with velocity 20 m/s. Maximum height reached (g=10 m/s²):
- Identify what the question tests: A ball is thrown vertically upward with velocity 20 m/s..
- Using the third equation of motion, the maximum height is calculated as u^2 / (2g), which yields 20^2 / 20 = 20 meters.
- Option D is incorrect because it mistakenly omits the factor of 2 in the denominator, doubling the actual height.
Traps the examiner sets
- Option D is incorrect because it mistakenly omits the factor of 2 in the denominator, doubling the actual height.
- Option B is incorrect because 50 J is obtained if you neglect the factor of 2 in the denominator, using p^2/m instead.
- Option C is incorrect because doubling the angle of projection does not double the range.
- Option B is incorrect because 8 m/s would only be reached after 2 seconds of acceleration.
Test your recall
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