Answer:
v= 14 m/s
Explanation:
- Assuming no friction losses, the total mechanical energy must be conserved.
- At the top of the slide, all the energy is gravitational potential energy, as she starts at rest.
- At the bottom of the slide, if we choose this level as our zero reference level for the gravitational potential energy, all the energy will be purely kinetic.
- So, we can write the following equality:
- [tex]\Delta K + \Delta U =0[/tex]
    ⇒ΔK = -ΔU
    ⇒ [tex](\frac{1}{2}*m*v^{2}-0) =-(0- m*g*h) = m*g*h[/tex]
- Rearranging terms and simplifying we can solve for v, as follows:
    [tex]v_{f} = \sqrt{2*g*h} =\sqrt{2*9.8m/s2*10.0m} = 14 m/s[/tex]
- Katie's speed at the bottom of the slide will be 14 m/s.
