Question

Olympic skier Tina Maze skis down a steep slope that descends at an angle of 30∘ below the horizontal. The coefficient of sliding friction between her skis and the snow is 0.10.

I found Maze's acceleration which is 4.1 m/s^2. But how do you determine Maze's speed 4.0 s after starting?

Answer 1

To determine Tina Maze's speed after 4.0 seconds with a constant acceleration of 4.1 m/s², use the equation v = at, which yields a speed of 16.4 m/s.

Step-by-step explanation:

The student is asking how to determine the speed of Olympic skier Tina Maze 4.0 seconds after starting from rest, given a constant acceleration of 4.1 m/s2. To find the speed after a certain time with constant acceleration, we use the kinematic equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. Assuming Tina Maze starts from rest (u = 0), the equation simplifies to v = at.

Using the given values, the calculation becomes:
v = 4.1 m/s2 × 4.0 s = 16.4 m/s.

Tina Maze's speed after 4.0 seconds would therefore be 16.4 m/s.

Answer 2

net force on Maze during his sliding downwards motion

`F = mgsin30 - \mu mg cos30`

now we will have

`F = mg(sin30 - 0.10cos30)`

now to find the acceleration we will have

`a = (F)/(m)`

`a = g(sin30 - 0.10cos30)`

`a = 9.81(0.5 - 0.10(0.866))`

`a = 4.1 m/s^2`

now to find the speed after 4 s is given by kinematics

`v_f - v_i = at`

here we know that

`v_i = 0`

`v_f - 0 = 4.1(4)`

`v_f = 16.22 m/s`

so Maze speed after 4 s will be 16.22 m/s