# Using linear kinematics to determine time and distance

1 A skier is gliding along at 2.08 m/s on horizontal, frictionless snow. He suddenly starts down a 14.2° incline. His speed at the bottom is 23.7 m/s. What is the length of the incline.

2 How long does it take him to reach the bottom?

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#### Solution Preview

I have drawn a diagram to ease understanding {SEE ATTACHMENT}

We have to resolve the accelerations and velocities we know into vector components aligned with the slope

The vector component due to the earths gravity along the slope (call it a) is as given by (1) below.

a = g.Sin{14.2} (1)

We now need to find the component of the initial horizontal velocity along the slope (call it u(slope)) this can be given by examining the triangular construction I have shown to be given by (2) as

u(slope) = u.Cos{14.2} (2)

Now that we have the components of the ...

#### Solution Summary

Analysis of a skiers trek down a slope using linear kinematic equations and techniques