A particle is moving vertically in a resistive medium under the influence of gravity - HSC - SSCE Mathematics Extension 2 - Question 10 - 2022 - Paper 1
Question 10
A particle is moving vertically in a resistive medium under the influence of gravity. The resistive force is proportional to the velocity of the particle.
The initi... show full transcript
Worked Solution & Example Answer:A particle is moving vertically in a resistive medium under the influence of gravity - HSC - SSCE Mathematics Extension 2 - Question 10 - 2022 - Paper 1
Step 1
If the particle is initially moving downwards, then its speed will increase.
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Answer
This statement is false. When moving downwards in a resistive medium, the resistive force opposes the motion, leading to a decrease in speed.
Step 2
If the particle is initially moving downwards, then its speed will decrease.
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Answer
This statement is true. The resistive force acting against the downward motion causes the speed to decrease as the particle moves.
Step 3
If the particle is initially moving upwards, then its speed will eventually approach a terminal speed.
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Answer
This statement is true. When moving upwards, the particle will also face a resistive force. Eventually, the upward speed will decrease until it reaches a terminal speed, where the forces balance.
Step 4
If the particle is initially moving upwards, then its speed will not eventually approach a terminal speed.
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Answer
This statement is false. Regardless of the initial direction, the movement through a resistive medium will lead to the establishment of a terminal speed.
