"If a skier coasts down a slope at an angle of 24 degrees below the horizontal, what is her acceleration if the force of friction is negligible?"

Question

I must have done this question 15 times, and still can't get the right anwser. Can anyone help me?

Answer 1

say she has mass m
there is a gravitational force down on her = m g
that force has a component normal (perpendicular) to the snow)=mg cos 24
there is an equal and opposite force up from the snow = mg cos 24
because there is no acceleration into or out of the snow.
HOWEVER, that gravitational force has another component down the slope = m g sin 24
There is no equal and opposite force to resist that because she is free to accelerate down the slope.
so
F = m a = m g sin 24
so
a = g sin 24
g is about 9.8 m/s^2
and sin 24 is about .407

Answer 2

Thank you so much; once I drew my slope levels correctly, it was no problem. Thanks again!