A boat of mass 700 ,kg is travelling at a spe | vedclass

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(D) Given: Mass of the boat, $m = 700 \,kg$. Initial speed, $v_1 = 24 \,ms^{-1}$. Final speed, $v_2 = 6 \,ms^{-1}$. Frictional force, $f = 35v$.Accord

Vedclass · Accepted Answer

$28$

Vedclass · Answer

(D) Given: Mass of the boat, $m = 700 \,kg$. Initial speed, $v_1 = 24 \,ms^{-1}$. Final speed, $v_2 = 6 \,ms^{-1}$. Frictional force, $f = 35v$.According to Newton's second law, the retarding force is $f = -m \frac{dv}{dt}$.Substituting the given values: $35v = -700 \frac{dv}{dt}$.Rearranging the terms: $\frac{dv}{v} = -\frac{35}{700} dt = -\frac{1}{20} dt$.Integrating both sides from $v_1$ to $v_2$ and $0$ to $t$: $\int_{24}^{6} \frac{dv}{v} = -\int_{0}^{t} \frac{1}{20} dt$.$\ln(\frac{6}{24}) = -\frac{t}{20}$.$\ln(\frac{1}{4}) = -\frac{t}{20}$.$-\ln(4) = -\frac{t}{20} \Rightarrow t = 20 \ln(4) = 20 \ln(2^2) = 40 \ln(2)$.Using $\ln(2) \approx 0.693$, $t = 40 	imes 0.693 = 27.72 \,s$.Rounding to the nearest integer, $t \approx 28 \,s$.

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