A projectile of mass 200 g is launched in a viscous medium at an angle 45° with the horizontal, with an initial velocity of 270 m / s . It experiences a viscous drag force F = − c v where the drag coe

Question

A projectile of mass 200 g is launched in a viscous medium at an angle 45° with the horizontal, with an initial velocity of $270 m / s$ . It experiences a viscous drag force $F = - c v$ where the drag coefficient $C = 0.2 kg / s$ and $v$ is the instantaneous velocity of the projectile. The projectile hits a vertical wall after 2 s. Taking $e = 2.7$ , the horizontal distance of the wall from the point of projection (in m) is $____$ .

Answer:

164.00

Solution:

$m \frac{d v _{x}}{d t} = - C v_{x}$

$v_{x} = v_{0 x} e^{- Ct / m}$

$S_{x} = \frac{m v _{0 x}}{C} (1 - e^{- Ct / m})$

$m = C = 0.2, v_{0 x} = 270/ 2, t = 2$

$S_{x} \approx 165.08 m$

TestHub · Accepted Answer

m d t d v x ​ ​ = − C v x ​ v x ​ = v 0 x ​ e − Ct / m S x ​ = C m v 0 x ​ ​ ( 1 − e − Ct / m ) m = C = 0.2 , v 0 x ​ = 270/ 2 ​ , t = 2 S x ​ ≈ 165.08 m

Physics - Kinematics Question with Solution | TestHub

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