A snowboarder and her board (combined mass 40.0 kgkg) are moving at 9.30 m/sm/s at the bottom of a curved ditch. If friction can be ignored, what is the maximum vertical distance that she can travel up the sides of the ditch?

Explanation:

Since energy is conserved

Then, the kinetic energy is transformed to kinetic energy.

So Kinetic energy is given as

K.E=½mv²

And the potential energy is given as

P.E=mgh

Since, P.E=K.E

Then,

mgh=½mv²

Divide through by m

gh=½v²

Multiply through by 2

2gh=v²

Then, h=v²/2g

Given that,

The velocity is v=9.3m/s

And g is acceleration due to gravity g=9.81m/s²

So applying this, h=v²/2g

h=9.3²/2×9.81

h=4.41m

The maximum height reached is 4.41m.