A skier of mass m = 55kg glides down a slope at angle theta = 32∘, as shown in the figure below. The snow is so slippery that you can neglect friction.
Find the skier's acceleration.
Express your answer using two significant figures.
Find the force the snow exerts on the skier.
Express your answer using two significant figures.
Yo dude I'm working on the same one
To find the skier's acceleration, we can use the force equation:
F = m * a
where F is the net force acting on the skier, m is the mass of the skier, and a is the acceleration.
In this case, the only force acting on the skier is the component of the force of gravity acting parallel to the slope. We can calculate this force using trigonometry:
F_parallel = m * g * sin(theta)
where g is the acceleration due to gravity and theta is the angle of the slope.
Now we can substitute this force into the force equation:
m * a = m * g * sin(theta)
We can cancel out the mass on both sides of the equation:
a = g * sin(theta)
Now we can plug in the given values:
g = 9.8 m/s^2 (acceleration due to gravity)
theta = 32 degrees (angle of the slope)
Using a scientific calculator, we can find:
a = 9.8 m/s^2 * sin(32 degrees) ≈ 5.01 m/s^2
So, the skier's acceleration is approximately 5.01 m/s^2.
To find the force the snow exerts on the skier, we can use the force equation again:
F = m * a
Plugging in the values:
F = 55 kg * 5.01 m/s^2 ≈ 275.55 N
So, the force the snow exerts on the skier is approximately 275.55 N.