A skier squats low and races down a 13 ◦ ski slope. During a 7 s interval, the skier accelerates at 4.2 m/s 2 .What is the vertical component of the skier’s acceleration? Answer in units of m/s 2
The vertical component of a is a*sin(16) = 3.6m/s^2*sin(16) = 0.9923m/s^2
The horizontal component = a*cos(16) = 3.6m/s^2*cos(16) = 3.4605m/s^2
Well, let me crunch the numbers and find the vertical component of the skier's acceleration... But while I do that, have you ever seen a clown try to ski? It's quite a sight! All those big shoes flapping around, trying to stay balanced on those skinny skis. Talk about a slippery slope! Anyway, let's get back to the question at hand.
To find the vertical component of the skier's acceleration, we need to use some trigonometry. Since the ski slope has an angle of 13 ◦, we can use the sine function to find the vertical component.
The formula is:
Vertical Component = Acceleration * sin(θ)
where θ is the angle of the slope. Plugging in the values we have:
Vertical Component = 4.2 m/s^2 * sin(13 ◦)
Using my trusty calculator, I find that the vertical component of the skier's acceleration is approximately 1.04 m/s^2. So there you have it, the answer is 1.04 m/s^2. Keep on skiing, my friend, and remember to steer clear of those clown skiers!
To find the vertical component of the skier's acceleration, we need to determine the component of the acceleration that acts vertically on the ski slope.
Given that the skier is racing down a 13° ski slope, we can use the angle to determine the vertical component of the acceleration.
The vertical component of the acceleration can be found using the formula:
Acceleration_vertical = Acceleration * sin(angle)
Given:
Acceleration = 4.2 m/s^2
Angle = 13°
Substituting the values into the formula:
Acceleration_vertical = 4.2 m/s^2 * sin(13°)
To calculate this, we need to convert the angle from degrees to radians.
Angle in radians = Angle in degrees * π / 180°
Therefore, the angle in radians is:
Angle in radians = 13° * π / 180°
Using the value of π (pi) as approximately 3.14159:
Angle in radians = 13° * 3.14159 / 180°
Now, calculate the sine of the angle:
sin(13°) = sin(Angle in radians)
Finally, substitute the calculated sine value into the equation for the vertical component of acceleration:
Acceleration_vertical = 4.2 m/s^2 * sin(Angle in radians)
After performing the calculations, the vertical component of the skier's acceleration is approximately 1.19 m/s^2.
To find the vertical component of the skier's acceleration, we need to determine the acceleration in the vertical direction.
Since the skier is moving down the slope, we can assume that the vertical direction is perpendicular to the slope. The 13° ski slope can be split into two components: the vertical component and the horizontal component.
The vertical component of the acceleration, denoted as a_y, can be calculated using the formula:
a_y = a * sin(θ)
where a is the total acceleration and θ is the angle of the slope.
In this case, the total acceleration a is given as 4.2 m/s^2 and the angle of the slope θ is given as 13°.
Using the formula, we can calculate the vertical component of acceleration:
a_y = 4.2 m/s^2 * sin(13°)
To find the sine of 13°, we can use a scientific calculator or online calculator. Plugging in the values, we get:
a_y = 4.2 m/s^2 * 0.22495105652
Evaluating the expression, we find:
a_y ≈ 0.943 m/s^2
Therefore, the vertical component of the skier's acceleration is approximately 0.943 m/s^2.