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Sagot :
Based on the data provided, the value of the constant b is 3.27 × 10^-5 kg/s and the time required to reach 63% of terminal velocity is 0.58 s.
What is terminal velocity?
The terminal velocity of a body is the velocity at which the body falls at constant velocity through a fluid.
For the falling raindrop, let positive direction be downwards and negative direction upwards,
- mass of the raindrop, m = 3×10-5 kg
- velocity at time t, is v(t)
- terminal velocity, v0 = 9 m/s
- gravitational acceleration, g = 9.81 m/s²
The raindrop experiences a downward gravitational force mg, and an upward drag force -bv.
The total force at a time t is given as
- F(t) = mg - bv(t)
a)
Terminal velocity is achieved then the total force is 0,
0 = mg - bv0
Therefore
b = mg/v0
Substitutingthe values:
b = (3 × 10^-5 × 9.8)/9
b = 3.27 × 10^-5 kg/s
b) Applying Newton's Second Law
F = ma
where
- a = v/t
- F = mg
Therefore,
mg = mv/t t = v/g
however, t is at 63% velocity
thus:
t = 0.63v/g
t = 0.63 × 9 /9.8
t = 0.58 s
Therefore, the value of the constant b is 3.27 × 10^-5 kg/s and the time required to reach 63% of terminal velocity is 0.58 s
Learn more about terminal velocity at: https://brainly.com/question/12903433
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