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A ball is dropped from the top of the tower 100m high. Simultaneously another ball is thrown upward with the speed of 50m/s .After what time do they cross each other ?
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A ball is dropped from the top of the tower 100m high. Simultaneously ...
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A ball is dropped from the top of the tower 100m high. Simultaneously ...
Understanding the Scenario
A ball is dropped from a height of 100m, while another is thrown upwards with an initial velocity of 50m/s. We need to determine the time at which these two balls cross each other.
Equations of Motion
To solve this, we can use the equations of motion.
1. For the dropped ball:
- Initial velocity (u) = 0 m/s
- Distance fallen (s) = 100 - h (where h is the height above the ground)
- Acceleration (a) = 9.8 m/s² (due to gravity)
- The equation is:
s = ut + (1/2)at²
So, h = 100 - (0*t + (1/2) * 9.8 * t²)
=> h = 100 - 4.9t²
2. For the thrown ball:
- Initial velocity (u) = 50 m/s
- Distance moved upwards (s) = h
- Acceleration (a) = -9.8 m/s² (acting downwards)
- The equation is:
h = ut + (1/2)at²
=> h = 50t - (1/2) * 9.8 * t²
=> h = 50t - 4.9t²
Setting the Heights Equal
To find the time when the balls cross, set the heights equal:
100 - 4.9t² = 50t - 4.9t²
This simplifies to:
100 = 50t
Calculating Time
Solving for t gives:
t = 100 / 50 = 2 seconds
Conclusion
The two balls cross each other after 2 seconds. This means the downward ball has fallen for 2 seconds and the upward ball has risen for the same duration.
A ball is dropped from a height of 100m, while another is thrown upwards with an initial velocity of 50m/s. We need to determine the time at which these two balls cross each other.
Equations of Motion
To solve this, we can use the equations of motion.
1. For the dropped ball:
- Initial velocity (u) = 0 m/s
- Distance fallen (s) = 100 - h (where h is the height above the ground)
- Acceleration (a) = 9.8 m/s² (due to gravity)
- The equation is:
s = ut + (1/2)at²
So, h = 100 - (0*t + (1/2) * 9.8 * t²)
=> h = 100 - 4.9t²
2. For the thrown ball:
- Initial velocity (u) = 50 m/s
- Distance moved upwards (s) = h
- Acceleration (a) = -9.8 m/s² (acting downwards)
- The equation is:
h = ut + (1/2)at²
=> h = 50t - (1/2) * 9.8 * t²
=> h = 50t - 4.9t²
Setting the Heights Equal
To find the time when the balls cross, set the heights equal:
100 - 4.9t² = 50t - 4.9t²
This simplifies to:
100 = 50t
Calculating Time
Solving for t gives:
t = 100 / 50 = 2 seconds
Conclusion
The two balls cross each other after 2 seconds. This means the downward ball has fallen for 2 seconds and the upward ball has risen for the same duration.
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A ball is dropped from the top of the tower 100m high. Simultaneously another ball is thrown upward with the speed of 50m/s .After what time do they cross each other ?
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A ball is dropped from the top of the tower 100m high. Simultaneously another ball is thrown upward with the speed of 50m/s .After what time do they cross each other ? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about A ball is dropped from the top of the tower 100m high. Simultaneously another ball is thrown upward with the speed of 50m/s .After what time do they cross each other ? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A ball is dropped from the top of the tower 100m high. Simultaneously another ball is thrown upward with the speed of 50m/s .After what time do they cross each other ?.
A ball is dropped from the top of the tower 100m high. Simultaneously another ball is thrown upward with the speed of 50m/s .After what time do they cross each other ? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about A ball is dropped from the top of the tower 100m high. Simultaneously another ball is thrown upward with the speed of 50m/s .After what time do they cross each other ? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A ball is dropped from the top of the tower 100m high. Simultaneously another ball is thrown upward with the speed of 50m/s .After what time do they cross each other ?.
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