A 75-kg person on skis is going down a hill sloped at 30.0°. The coefficient of kinetic friction between the skis and the snow is 0.15. How fast is the skier going 10.0 s after starting from rest?
I want to know how to solve this and answer pls!
fyk
To find the speed of the skier 10.0 seconds after starting from rest, we need to analyze the forces acting on the skier.
First, let's calculate the gravitational force acting on the skier:
Gravitational force = mass x acceleration due to gravity
Gravitational force = 75 kg x 9.8 m/s^2
Gravitational force = 735 N
Next, let's calculate the force of friction between the skis and the snow:
Force of friction = coefficient of kinetic friction x Normal force
Normal force = mass x gravitational acceleration x cosine(30°)
Normal force = 75 kg x 9.8 m/s^2 x cos(30°)
Normal force = 637.5 N
Force of friction = 0.15 x 637.5 N
Force of friction = 95.625 N
Now, let's calculate the net force acting on the skier:
Net force = Gravitational force - Force of friction
Net force = 735 N - 95.625 N
Net force = 639.375 N
Using Newton's second law of motion, we can find the acceleration of the skier:
Net force = mass x acceleration
639.375 N = 75 kg x acceleration
Acceleration = 639.375 N / 75 kg
Acceleration = 8.525 m/s^2
Finally, let's find the speed of the skier after 10.0 seconds:
Speed = initial velocity + (acceleration x time)
Since the skier starts from rest, the initial velocity is 0.
Speed = 0 + (8.525 m/s^2 x 10.0 s)
Speed = 85.25 m/s
Therefore, the skier is going at a speed of 85.25 m/s after 10.0 seconds.
To determine the speed of the skier 10.0 seconds after starting from rest, we need to consider the forces acting on the skier.
First, let's find the gravitational force pulling the skier downhill. The gravitational force can be calculated using the equation:
F_gravity = m * g
where
m = mass of the skier = 75 kg (given)
g = acceleration due to gravity = 9.8 m/s²
Plugging in the values, we get:
F_gravity = 75 kg * 9.8 m/s²
= 735 N
Next, let's find the force of kinetic friction acting on the skier, which opposes the motion. The force of kinetic friction can be calculated using the equation:
F_friction = μ * F_normal
where
μ = coefficient of kinetic friction = 0.15 (given)
F_normal = normal force
The normal force is the force exerted by a surface perpendicular to it. In this case, it is equal to the gravitational force pulling the skier downhill:
F_normal = F_gravity
= 735 N (as calculated earlier)
Plugging in these values, we get:
F_friction = 0.15 * 735 N
= 110.25 N
Now, let's find the net force acting on the skier. The net force is the vector sum of all the forces acting on the skier:
F_net = F_gravity - F_friction
Plugging in the values, we get:
F_net = 735 N - 110.25 N
= 624.75 N
Using Newton's second law of motion, we know that the net force is equal to the mass of the skier multiplied by the acceleration:
F_net = m * a
Rearranging the equation, we can calculate the acceleration:
a = F_net / m
= 624.75 N / 75 kg
= 8.33 m/s²
Knowing the acceleration, we can now find the final velocity of the skier using the equation of motion:
v = u + a * t
where
v = final velocity (unknown)
u = initial velocity (which is 0, as the skier starts from rest)
a = acceleration (as calculated earlier)
t = time = 10.0 s (given)
Plugging in the values, we get:
v = 0 + (8.33 m/s²) * 10.0 s
= 83.3 m/s
So, the skier will be going 83.3 m/s after 10.0 seconds from starting from rest.