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A kid of mass 30kg running with a speed. of 10 m/s jumps over a stationary card of mass5kg find the velocity of the kid and the cart after the jump?
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A kid of mass 30kg running with a speed. of 10 m/s jumps over a statio...
To solve the problem of a kid jumping over a stationary cart, we will apply the principle of conservation of momentum.
Understanding the Scenario
- Mass of the Kid (m1): 30 kg
- Velocity of the Kid before the jump (v1): 10 m/s
- Mass of the Cart (m2): 5 kg
- Velocity of the Cart before the jump (v2): 0 m/s
Initial Momentum Calculation
- Initial Momentum (p_initial):
p_initial = (m1 * v1) + (m2 * v2)
p_initial = (30 kg * 10 m/s) + (5 kg * 0 m/s)
p_initial = 300 kg·m/s
After the Jump
When the kid jumps over the cart, we assume there is no external force acting on the system, thus momentum is conserved. Let’s denote:
- Final Velocity of the Kid (v_kid): unknown
- Final Velocity of the Cart (v_cart): unknown
Using the conservation of momentum:
p_initial = p_final
300 kg·m/s = (m1 * v_kid) + (m2 * v_cart)
Assuming the Cart Moves
Assuming the kid jumps straight up and does not impart any horizontal velocity to the cart, the cart remains stationary. Thus, we can say:
v_cart = 0
Now, we can express the final momentum:
300 kg·m/s = (30 kg * v_kid) + (5 kg * 0)
300 kg·m/s = 30 kg * v_kid
v_kid = 10 m/s
Conclusion
- Final Velocity of the Kid: 10 m/s (the same as before the jump)
- Final Velocity of the Cart: 0 m/s (stationary)
In this case, the velocities remain unchanged for both the kid and the cart post-jump, as the jump does not exert any horizontal force on the cart.
Understanding the Scenario
- Mass of the Kid (m1): 30 kg
- Velocity of the Kid before the jump (v1): 10 m/s
- Mass of the Cart (m2): 5 kg
- Velocity of the Cart before the jump (v2): 0 m/s
Initial Momentum Calculation
- Initial Momentum (p_initial):
p_initial = (m1 * v1) + (m2 * v2)
p_initial = (30 kg * 10 m/s) + (5 kg * 0 m/s)
p_initial = 300 kg·m/s
After the Jump
When the kid jumps over the cart, we assume there is no external force acting on the system, thus momentum is conserved. Let’s denote:
- Final Velocity of the Kid (v_kid): unknown
- Final Velocity of the Cart (v_cart): unknown
Using the conservation of momentum:
p_initial = p_final
300 kg·m/s = (m1 * v_kid) + (m2 * v_cart)
Assuming the Cart Moves
Assuming the kid jumps straight up and does not impart any horizontal velocity to the cart, the cart remains stationary. Thus, we can say:
v_cart = 0
Now, we can express the final momentum:
300 kg·m/s = (30 kg * v_kid) + (5 kg * 0)
300 kg·m/s = 30 kg * v_kid
v_kid = 10 m/s
Conclusion
- Final Velocity of the Kid: 10 m/s (the same as before the jump)
- Final Velocity of the Cart: 0 m/s (stationary)
In this case, the velocities remain unchanged for both the kid and the cart post-jump, as the jump does not exert any horizontal force on the cart.
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A kid of mass 30kg running with a speed. of 10 m/s jumps over a stationary card of mass5kg find the velocity of the kid and the cart after the jump?
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A kid of mass 30kg running with a speed. of 10 m/s jumps over a stationary card of mass5kg find the velocity of the kid and the cart after the jump? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A kid of mass 30kg running with a speed. of 10 m/s jumps over a stationary card of mass5kg find the velocity of the kid and the cart after the jump? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A kid of mass 30kg running with a speed. of 10 m/s jumps over a stationary card of mass5kg find the velocity of the kid and the cart after the jump?.
A kid of mass 30kg running with a speed. of 10 m/s jumps over a stationary card of mass5kg find the velocity of the kid and the cart after the jump? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A kid of mass 30kg running with a speed. of 10 m/s jumps over a stationary card of mass5kg find the velocity of the kid and the cart after the jump? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A kid of mass 30kg running with a speed. of 10 m/s jumps over a stationary card of mass5kg find the velocity of the kid and the cart after the jump?.
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