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A ball is thrown upwards into air with a...

A ball is thrown upwards into air with a speed greater than its terminal speed. It lands at the same place from where it was thrown. Mark the correct statement (s).

A

a. It acquires terminal speed before it gets to the highest point of the trajectory.

B

b. Before reaching the highest point of trajectory, its speed is continuously decreasing.

C

c. During the entire flight, the force of air resistance is greatest just after it is down

D

d. The magnitude of net force experienced by the ball is maximum just after it is thrown.

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The correct Answer is:
To solve the problem, we need to analyze the motion of a ball thrown upwards with a speed greater than its terminal speed and determine which statements about its motion are correct. ### Step-by-Step Solution: 1. **Understanding Terminal Speed**: - Terminal speed is the constant speed that a freely falling object eventually reaches when the resistance of the medium (air resistance) prevents further acceleration. When the ball is thrown upwards with a speed greater than its terminal speed, it will initially accelerate upwards. 2. **Forces Acting on the Ball**: - When the ball is thrown upwards, two forces act on it: - Gravitational force (mg) acting downwards. - Air resistance (F_a) acting upwards, which is proportional to the velocity of the ball (F_a = k * v). - Initially, the ball has a large upward velocity, so the air resistance is also large, but it is still less than the gravitational force. 3. **Motion Upwards**: - As the ball moves upwards, its velocity decreases due to the net force acting downwards (mg + F_a). The speed of the ball continuously decreases until it reaches the highest point, where its velocity becomes zero. 4. **At the Highest Point**: - At the highest point, the velocity of the ball is zero. Therefore, it cannot have acquired terminal speed before reaching this point because terminal speed is a constant speed that occurs when the forces are balanced (when the net force is zero). 5. **Motion Downwards**: - After reaching the highest point, the ball starts descending. During this phase, the gravitational force (mg) acts downwards, and the air resistance (F_a) acts upwards. The ball will accelerate downwards until it reaches terminal speed, where the forces balance out. 6. **Analyzing the Statements**: - **Statement A**: "It acquires terminal speed before it gets to the highest point of the trajectory." - **Incorrect**: The ball cannot acquire terminal speed before reaching the highest point because at that point, its velocity is zero. - **Statement B**: "Before reaching the highest point of the trajectory, its speed continuously decreases." - **Correct**: The speed decreases as the ball moves upwards due to the net downward force. - **Statement C**: "During the entire flight, the force of air resistance is greatest just after it is thrown." - **Correct**: The air resistance is proportional to velocity, which is maximum just after the ball is thrown. - **Statement D**: "The magnitude of the net force experienced by the ball is maximum just after it is thrown." - **Correct**: The net force is maximum just after the throw because the gravitational force is at its maximum and the air resistance is also significant at that moment. ### Conclusion: The correct statements are: - Statement B - Statement C - Statement D

To solve the problem, we need to analyze the motion of a ball thrown upwards with a speed greater than its terminal speed and determine which statements about its motion are correct. ### Step-by-Step Solution: 1. **Understanding Terminal Speed**: - Terminal speed is the constant speed that a freely falling object eventually reaches when the resistance of the medium (air resistance) prevents further acceleration. When the ball is thrown upwards with a speed greater than its terminal speed, it will initially accelerate upwards. 2. **Forces Acting on the Ball**: ...
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