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A particle is projected vertically upward with speed u = 10m/s. During its journey air applies a force of -0.2v^2 on the particle. what is the maximum height attained by the particle? (m =2kg) a) 5 ln(2) b) 3 ln(2). c) 2 ln(2) d) 10 ln(2)?
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A particle is projected vertically upward with speed u = 10m/s. During...
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A particle is projected vertically upward with speed u = 10m/s. During...


Given data:
- Initial velocity (u) = 10 m/s
- Force due to air resistance = -0.2v^2
- Mass of the particle (m) = 2 kg

Calculating the maximum height:
To find the maximum height attained by the particle, we need to analyze the forces acting on it.

1. Net Force:
The net force acting on the particle can be given by:
F_net = ma
Where F_net is the net force, m is the mass of the particle, and a is the acceleration.

2. Force due to air resistance:
The force due to air resistance is given by:
F_air = -0.2v^2
Where v is the velocity of the particle.

3. Net Force equation:
F_net = F - F_air
ma = -0.2v^2
a = -0.1v^2

4. Using kinematic equation:
The final velocity of the particle when it reaches maximum height is 0 m/s.
v^2 = u^2 + 2as
0 = 10^2 + 2*(-0.1)s
s = 50 m

5. Calculating the maximum height:
The maximum height attained by the particle can be calculated using the formula:
h = u^2/2g
h = 10^2 / (2*9.8) = 5.1 m

Therefore, the maximum height attained by the particle is approximately 5.1 meters.
The correct option is a) 5 ln(2).
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A particle is projected vertically upward with speed u = 10m/s. During its journey air applies a force of -0.2v^2 on the particle. what is the maximum height attained by the particle? (m =2kg) a) 5 ln(2) b) 3 ln(2). c) 2 ln(2) d) 10 ln(2)?
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