A skier is accelerating down a 30.0° hill at a = 3.70 m/s2 (

(a) What is the vertical component of her acceleration?


|m/s2 (downward)

(b) How long will it take her to reach the bottom of the hill, assuming she starts from rest and accelerates uniformly, if the elevation change is 310 m?
s

vertical component? 3.70*sinTheta

b) distance= 310/sinTheta
distance= 1/2 a t^2 solve for t.

(a) To find the vertical component of the skier's acceleration, we need to determine the acceleration along the vertical direction. The vertical component of the acceleration can be found using the equation:

a_vertical = a * cos(theta)

where a is the skier's acceleration (given as 3.70 m/s^2) and theta is the angle of the hill (given as 30.0°).

First, we convert theta from degrees to radians by using the formula:

theta_radians = theta * (pi/180)

Substituting the values, we get:

theta_radians = 30.0° * (pi/180) = 0.5236 radians

Next, we can calculate the vertical component of acceleration:

a_vertical = 3.70 m/s^2 * cos(0.5236 radians) = 3.70 m/s^2 * 0.8660 ≈ 3.204 m/s^2

Therefore, the vertical component of the skier's acceleration is approximately 3.204 m/s^2 downward.

(b) To find the time it takes for the skier to reach the bottom of the hill, we can use the kinematic equation:

d = v_initial * t + (1/2) * a * t^2

where d is the elevation change (given as 310 m), v_initial is the initial velocity (which is 0 m/s since the skier starts from rest), a is the skier's acceleration (3.70 m/s^2), and t is the time.

Rearranging the equation to solve for time (t), we get:

t = sqrt((2 * d) / a)

Substituting the values, we get:

t = sqrt((2 * 310 m) / 3.70 m/s^2) = sqrt(840) ≈ 28.99 s

Therefore, it will take the skier approximately 28.99 seconds to reach the bottom of the hill.