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An object falling from rest in air is su...

An object falling from rest in air is subject not only to the gravitational force but also to air resistance. Assume that the air resistance is proportional to the velocity with constant of proportionality as `k >0` , and acts in a direction opposite to motion `(g=9. 8 m/(s^2))dot` Then velocity cannot exceed. `( a ) 9.8m//k" "m//s ` (b) ` 98//km" "m//s` (c) k/g m/s (d) None of these

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To solve the problem, we need to analyze the forces acting on the object falling through the air. The object experiences two main forces: the gravitational force acting downward and the air resistance acting upward. ### Step-by-Step Solution: 1. **Identify the Forces**: - The gravitational force acting on the object is given by \( F_g = mg \), where \( m \) is the mass of the object and \( g = 9.8 \, \text{m/s}^2 \). - The air resistance force is proportional to the velocity \( v \) and is given by \( F_r = kv \), where \( k > 0 \) is the constant of proportionality. ...
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