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A 60 kg skier with an initial speed of 16 m/s Coasts up a 2.5 m high rise as shown. Find her final speed at the top in meters per second, given that the ice ground is frictionless

A 60 kg skier with an initial speed of 16 m/s Coasts up a 2.5 m high rise as shown-example-1
User BerggreenDK
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1 Answer

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13 votes

This problem relies on the law of conservation of energy

The equation below is the formula for kinetic energy


KE=(1)/(2)mv^2

And the formula for gravitational potential energy is


PE=mgh

So to find final speed, we will use both of these formulas


(1)/(2)mv_1^2+mgh_1=(1)/(2)mv_2^2+mgh_2
(1)/(2)mv_1^2+mgh_1=(1)/(2)mv_2^2+mgh_2

This formula gives us the energy before and after the skier moves up the hill.

For variables, we have

v1 = 16 m/s

mass = 60 Kg

h2 = 2.5 m

h1 = 0 m


\begin{gathered} (1)/(2)(60)(16)^2+(60)g(0)=(1)/(2)(60)(v_2)^2+(60)g(2.5) \\ 256=v_2^2+49 \\ v_2^2=207 \\ v_2=14.38\text{ }(m)/(s) \end{gathered}

Final Velocity is 14.38 m/s

User Wiktoria
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