Final answer:
To find the speed of the skier after 4.0 seconds, you can calculate the acceleration using the equation a = g*sin(θ) - μ*g*cos(θ) and then use the formula v = u + a*t to find the final velocity. The final velocity of the skier after 4.0 seconds is 7.71 m/s.
Step-by-step explanation:
To find the speed of the skier after 4.0 seconds, we need to calculate the acceleration first. The equation for the acceleration of the skier on a slope is:
a = g*sin(θ) - μ*g*cos(θ)
Where:
- a is the acceleration
- g is the acceleration due to gravity (9.8 m/s^2)
- θ is the angle of the slope (34 degrees)
- μ is the coefficient of kinetic friction (0.17)
Substituting the values into the equation, we get:
a = (9.8 m/s^2)*sin(34) - (0.17)*(9.8 m/s^2)*cos(34)
Then, we can use the acceleration to find the final velocity of the skier using the formula:
v = u + a*t
Where:
- v is the final velocity
- u is the initial velocity (0 m/s, since the skier starts from rest)
- a is the acceleration
- t is the time (4.0 seconds)
Substituting the values into the equation, we get:
v = 0 + (9.8 m/s^2)*sin(34)*4.0 s - (0.17)*(9.8 m/s^2)*cos(34)*4.0 s
Simplifying the equation, the final velocity of the skier after 4.0 seconds is 7.71 m/s.