Question

How long will it take an athlete to run 300m at a gradient of 1:10 if he can run 300m in 60 sec on a flat surface. Weather is a constant.

Answer 1

$$s=0.5at^2$$

$$a=\frac{2s}{t^2}$$

$$a'=a-g\sin{\alpha}=a-0.1g$$

$$t'=\sqrt{\frac{2s}{a'}}=\sqrt{\frac{2s}{a-0.1g}}=\sqrt{\frac{2s}{\frac{2s}{t^2}-0.1g}}$$

$$t'=t\sqrt{\frac{1}{1-\frac{0.1gt^2}{2s}}}=60\sqrt{\frac{1}{1-\frac{0.1(9.8)(60)^2}{2(300)}}}=93\ s$$