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A girl of mass 20 kg having velocity 2 m/sec jumps on stationary cart of mass 2 kg. Find the velocity of the girl when the cart starts moving
- a)2 m/s
- b)54 m/s
- c)0.95 m/s
- d)1.81 m/s
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
A girl of mass 20 kg having velocity 2 m/sec jumps on stationary cart...
To solve this problem, we can use the principle of conservation of momentum. This principle states that the total momentum before an event is equal to the total momentum after the event, as long as no external forces are acting on the system.
Let's break down the problem into two parts: before the girl jumps onto the cart and after she jumps onto the cart.
Before the girl jumps:
- Girl's mass (m1) = 20 kg
- Girl's velocity (v1) = 2 m/s
- Cart's mass (m2) = 2 kg (stationary, so its velocity is 0)
After the girl jumps:
- Girl's mass (m1) = 20 kg
- Girl's velocity (v1') = ?
- Cart's mass (m2) = 2 kg
- Cart's velocity (v2') = ?
Using the principle of conservation of momentum, we can write the equation:
(m1 * v1) + (m2 * 0) = (m1 * v1') + (m2 * v2')
Simplifying the equation, we get:
(m1 * v1) = (m1 * v1') + (m2 * v2')
Plugging in the values, we have:
(20 kg * 2 m/s) = (20 kg * v1') + (2 kg * v2')
Simplifying further, we have:
40 kg m/s = 20 kg * v1' + 2 kg * v2'
Since the cart starts moving, its velocity (v2') is not zero. Therefore, we can rewrite the equation as:
40 kg m/s = 20 kg * v1' + 2 kg * v2'
To find the velocity of the girl when the cart starts moving (v1'), we need to know the value of v2'. Unfortunately, the problem does not provide this information.
Therefore, we cannot determine the exact velocity of the girl when the cart starts moving. The correct answer should be option 'Cannot be determined' or 'Insufficient information provided'. The given options do not include this choice, so none of them is correct.
Let's break down the problem into two parts: before the girl jumps onto the cart and after she jumps onto the cart.
Before the girl jumps:
- Girl's mass (m1) = 20 kg
- Girl's velocity (v1) = 2 m/s
- Cart's mass (m2) = 2 kg (stationary, so its velocity is 0)
After the girl jumps:
- Girl's mass (m1) = 20 kg
- Girl's velocity (v1') = ?
- Cart's mass (m2) = 2 kg
- Cart's velocity (v2') = ?
Using the principle of conservation of momentum, we can write the equation:
(m1 * v1) + (m2 * 0) = (m1 * v1') + (m2 * v2')
Simplifying the equation, we get:
(m1 * v1) = (m1 * v1') + (m2 * v2')
Plugging in the values, we have:
(20 kg * 2 m/s) = (20 kg * v1') + (2 kg * v2')
Simplifying further, we have:
40 kg m/s = 20 kg * v1' + 2 kg * v2'
Since the cart starts moving, its velocity (v2') is not zero. Therefore, we can rewrite the equation as:
40 kg m/s = 20 kg * v1' + 2 kg * v2'
To find the velocity of the girl when the cart starts moving (v1'), we need to know the value of v2'. Unfortunately, the problem does not provide this information.
Therefore, we cannot determine the exact velocity of the girl when the cart starts moving. The correct answer should be option 'Cannot be determined' or 'Insufficient information provided'. The given options do not include this choice, so none of them is correct.
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Community Answer
A girl of mass 20 kg having velocity 2 m/sec jumps on stationary cart...
If the two bodies stick to each other after
collision, they will move with a common velocity v given by
V =maua + mbub/ma + mb
Here, ma = 20 kg, ua = 2 m/s, mb = 2 kg, ub = 0
∴ v = 20 × 2 +2 × 0/20+2 = 40/22 = 1.81 m/s
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A girl of mass 20 kg having velocity 2 m/sec jumps on stationary cart of mass 2 kg. Find the velocity of the girl when the cart starts movinga)2 m/sb)54 m/sc)0.95 m/sd)1.81 m/sCorrect answer is option 'D'. Can you explain this answer?
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