Downhill Skiing

#635 / Dynamics Easy

Going straight downhill, a skier traverses a mountain slope with a constant acceleration, passing a fork in the route first, then a tree 100 meters later. If the skier passes the tree 5 seconds after the fork in the slope with a velocity of 10 m/s, what is the skier’s acceleration?

Expand Hint
$$$s=\frac{1}{2}a_0(t^2)+v(t)$$$
where $$v$$ is the velocity along the direction of travel, $$a_0$$ is constant acceleration, and $$s$$ is the displacement at time $$t$$ along the line of travel.
Hint 2
Solve for $$a_0$$ .
For constant acceleration, the equation for displacement as a function of time:
$$$s=\frac{1}{2}a_0(t^2)+v(t)$$$
where $$v$$ is the velocity along the direction of travel, $$a_0$$ is constant acceleration, and $$s$$ is the displacement at time $$t$$ along the line of travel.

Solving for acceleration:
$$$100m=\frac{1}{2}a_0(5s)^2+10\frac{m}{s}(5s)$$$
$$$100m=\frac{1}{2}a_0(25s^2)+50m$$$
$$$a_0=\frac{50m(2)}{25s^2}=4\:m/s^2$$$
$$$4\:m/s^2$$$


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