Question

An athlete reaches the finish line at a velocity of 33 m s−1. She then applies a minimum braking force of 240 N as she moves along the uphill section of track to help her come to a stop.

Calculate the minimum uphill length of track L that should be available for braking. You should ignore all frictional forces other than those applied by the athlete.

mass of sledge and athlete = 95 kg

Answer 1

$ma=-F_{br}=-240$ N

$mv=-F_{br}t+c$

for t=0:

$v_0=33\ m/s \implies c=v_0m$

$mL=-F_{br}t^2/2+v_0mt$

$L(t)=-F_{br}t^2/(2m)+v_0t$

$L'(t)=F_{br}t/m+v_0=0$

$t=mv_0/F_{br}=95\cdot 33/240=13$ s

$L_{min}=33\cdot 13-240\cdot 13^2/(2\cdot 95)=215.5$ m