Rates of Change - Is this answer correct?

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The problem involves calculating the time it takes for an oil droplet with a radius increasing at 0.5 m/s to reach the edge of a circular container with a radius of 50 m. The formula T = R/r is applied, leading to the conclusion that it will take 100 seconds for the droplet to reach the container's sides. A user humorously notes their lack of math skills despite successfully performing the calculations. The discussion highlights the straightforward nature of the math involved, reinforcing that even those who claim not to understand math can arrive at correct answers. Overall, the solution confirms that the initial calculation of 100 seconds is indeed correct.
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Homework Statement



A droplet of oil is placed at the bottom of a circular container of radius(R)= 50m so that it is in the centre. If the radius (r) of the droplet is increasing at a constant rate of 0.5ms^-1. How long will it take for the droplet to reach the sides of the container i.e.when R=r.

Homework Equations



T=x/y=R/r where T=time, x=radius of container, y=radius of droplet.

The Attempt at a Solution



t=50/0.5=100s?

I don't do maths so I thought maybe you guys could help.

Thanks a lot.
 
Physics news on Phys.org
If you walk a half a meter per second how far will you go in 1, 10, and 100 seconds?

.5m, 5m, 50m ?

You don't do math, you just did math!
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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