The safe radius, v m/s, at which a train can round a curve of radius r is directly proportional to the square root of r. It is given that the safe speed at which a train can round a curve of radius 256 m is 80 m/s. find the safe speed if the curve has a radius of 225 m.

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The safe radius, v m/s, at which a train can round a curve of radius r is directly proportional to the square root of r. It is given that the safe speed at which a train can round a curve of radius 256 m is 80 m/s. find the safe speed if the curve has a radius of 225 m.

since safe velocity (v) is directly proportional to the square root of radius (r), so we can conclude that

v=ccdotsqrt{r}

whereas c is particular constant related to the equation.

Now, by substituing v=80 and r=256 we will find out the constant c

begin{aligned}v&=ccdotsqrt{r}\80&=ccdotsqrt{256}\80&=ccdot16\therefore c&=5end{aligned}

Now, for r=225 m, we have

begin{aligned}v&=ccdotsqrt{r}\&=5cdotsqrt{225}\&=5cdot15\&=75end{aligned}

So, the safe velocity for radius 225 m is 75 m/s

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