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A body, thrown upwards with some velocity, reaches the maximum height of 20 m. Another body with double the mass thrown up, with double initial velocity will reach a maximum height of
- a)200 m
- b)16 m
- c)80 m
- d)40 m
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A body, thrown upwards with some velocity, reaches the maximum height ...
**Explanation:**
To solve this problem, we can use the principles of projectile motion and the conservation of energy.
**Projectile Motion:**
When a body is thrown upwards, it follows a parabolic path known as projectile motion. The body goes up to a certain height, reaches its maximum height, and then falls back down.
**Conservation of Energy:**
According to the principle of conservation of energy, the total mechanical energy of a system remains constant if there are no external forces acting on it. In the absence of air resistance, the only forces acting on the body are gravity and initial velocity.
**Calculating the Maximum Height:**
Let's assume the initial velocity of the first body is "v" and its mass is "m". The initial velocity of the second body will be "2v" and its mass will be "2m".
The maximum height reached by the first body can be calculated using the equation:
h = (v^2) / (2g)
where h is the maximum height, v is the initial velocity, and g is the acceleration due to gravity.
Substituting the given values, we get:
20 = (v^2) / (2g) --(1)
Similarly, the maximum height reached by the second body can be calculated using the equation:
h' = ((2v)^2) / (2g)
Simplifying this equation, we get:
h' = (4v^2) / (2g)
= (2v^2) / (g)
Comparing h' with h, we can see that h' is 2 times h.
**Answer:**
Therefore, the second body with double the mass and double the initial velocity will reach a maximum height of 80 m (option C).
To solve this problem, we can use the principles of projectile motion and the conservation of energy.
**Projectile Motion:**
When a body is thrown upwards, it follows a parabolic path known as projectile motion. The body goes up to a certain height, reaches its maximum height, and then falls back down.
**Conservation of Energy:**
According to the principle of conservation of energy, the total mechanical energy of a system remains constant if there are no external forces acting on it. In the absence of air resistance, the only forces acting on the body are gravity and initial velocity.
**Calculating the Maximum Height:**
Let's assume the initial velocity of the first body is "v" and its mass is "m". The initial velocity of the second body will be "2v" and its mass will be "2m".
The maximum height reached by the first body can be calculated using the equation:
h = (v^2) / (2g)
where h is the maximum height, v is the initial velocity, and g is the acceleration due to gravity.
Substituting the given values, we get:
20 = (v^2) / (2g) --(1)
Similarly, the maximum height reached by the second body can be calculated using the equation:
h' = ((2v)^2) / (2g)
Simplifying this equation, we get:
h' = (4v^2) / (2g)
= (2v^2) / (g)
Comparing h' with h, we can see that h' is 2 times h.
**Answer:**
Therefore, the second body with double the mass and double the initial velocity will reach a maximum height of 80 m (option C).
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A body, thrown upwards with some velocity, reaches the maximum height of 20 m. Another body with double the mass thrown up, with double initial velocity will reach a maximum height ofa)200 mb)16 mc)80 md)40 mCorrect answer is option 'C'. Can you explain this answer?
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