Calculate the final speed of a skier who skis down a 70.8 m high hill, if

her initial speed is 2.18 m/s

V^2 = Vo^2 + 2g*h

Vo = 2.18 m/s.
g = +9.8 m/s^2
h = 70.8 m.
Solve for V.

37.31531083

To calculate the final speed of the skier, we can use the principle of conservation of energy. The initial potential energy of the skier at the top of the hill will be converted to kinetic energy at the bottom of the hill.

The potential energy (PE) at the top of the hill can be calculated using the formula:

PE = m * g * h

where m is the mass of the skier, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height of the hill.

The kinetic energy (KE) at the bottom of the hill is given by the formula:

KE = 1/2 * m * v^2

where v is the final speed of the skier.

According to the conservation of energy, the initial potential energy will be equal to the final kinetic energy:

PE = KE

m * g * h = 1/2 * m * v^2

Simplifying the equation, we can cancel out the mass (m) on both sides:

g * h = 1/2 * v^2

v^2 = 2 * g * h

Taking the square root of both sides to isolate v:

√(v^2) = √(2 * g * h)

v = √(2 * g * h)

Now we can plug in the given values to find the final speed:

v = √(2 * 9.8 m/s^2 * 70.8 m)

Calculating this, we get:

v ≈ 23.7 m/s

Therefore, the skier's final speed will be approximately 23.7 m/s.