Santa loses his footing and slides down a frictionless, snowy roof that is tilted at an angle of 30.0. If Santa slides 5.00 before reaching the edge, what is his speed as he leaves the roof?

Answer 1

We can use the conservation of energy principle to solve this problem. We'll equate the initial potential energy (when Santa is at the top of the roof) with the final kinetic energy (when Santa is at the edge of the roof).

Initially, Santa is at a height h above the ground. We can find this height using trigonometry with the given roof angle and the distance he slides.

h = 5.00 m * sin(30.0°)

h ≈ 2.50 m

The potential energy (PE) at the top is given by:

PE_initial = m * g * h

And the final kinetic energy (KE) is given by:

KE_final = 1/2 * m * v^2

Equating initial potential energy with final kinetic energy:

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

Where m is the mass of Santa, g is the acceleration due to gravity (9.81 m/s²), and v is the final speed we want to find. The mass of Santa will cancel out:

g * h = 1/2 * v^2

Now we can solve for v:

v^2 = 2 * g * h
v^2 ≈ 2 * 9.81 m/s² * 2.50 m
v^2 ≈ 49.05 m²/s²

Taking the square root of both sides:

v ≈ 7.00 m/s

So Santa's speed as he leaves the roof is approximately 7.00 m/s.