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(d) At the Olympic $50m$ freestyle final, a camera is positioned at a distance of $10m$ from the lane at the half-way point. If the speed of a swimmer is $2m/s$, how quickly must the angle of the camera change to track the swimmer when the swimmer is at the $35m$ mark? The length of the pool is $50m$.
(c) The line density of a tapered metal bar is given by the formula $ρ(x)=10+xsin_{2}(x) $ in units of $kg/m$, where $x$ is the distance along the bar in metres. The first moment of mass of the bar is given $M_{0}=L1 ∫_{0}xρ(x)dx,$ where $L$ is the length of the bar. Compute the value of $M$ if $L=5m$.

Let the distance traveled by swimmer be .

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