Annie rides her snowboard down a hill sloped at 25 degrees. The coefficient of kinetic friction between her and her skies is .15. If her mass is 55 kg, hw fast is she excelerating? Assuming she starts from rest and the equation is v=v+a*t, what is her velocity after 7 seconds?
How do you solve for the acceleration at an incline?
I got that the acceleration is 5.6 meters per seconds sqaured because 308.7N/55kg.
Therefore, the final velocity is 39.2 meters per second.
IS THIS RIGHT?
Thanks all for your help!
What mass of water will give 240 calories when its temperature droped from 80 degrees celsius to 68 degrees celsius?
To solve for the acceleration of Annie on an incline, we can use the following formula:
a = g * sinθ - (μk * g * cosθ)
Where:
a = acceleration
g = acceleration due to gravity (approximately 9.8 m/s^2)
μk = coefficient of kinetic friction
θ = angle of the incline (25 degrees in this case)
Now let's substitute the given values into the formula:
a = (9.8 m/s^2) * sin(25°) - (0.15 * 9.8 m/s^2) * cos(25°)
Calculating each term separately:
a = (9.8 m/s^2) * 0.42262 - (0.15 * 9.8 m/s^2) * 0.90631
≈ 4.148 m/s^2 - 1.331 m/s^2
≈ 2.817 m/s^2
Therefore, the acceleration of Annie on the incline is approximately 2.817 m/s^2.
Now let's calculate her velocity after 7 seconds using the equation v = v0 + a * t.
Given:
Initial velocity (v0) = 0 (since she starts from rest)
Acceleration (a) = 2.817 m/s^2
Time (t) = 7 seconds
Using the equation:
v = 0 + (2.817 m/s^2) * 7 s
≈ 19.719 m/s
Therefore, Annie's velocity after 7 seconds is approximately 19.719 m/s.
To solve for the acceleration of Annie riding her snowboard down an inclined hill, you need to consider the forces acting on her. In this case, the main forces are the gravitational force (mg) pulling her down the slope and the force of kinetic friction (fk) opposing her motion. The equation to calculate the acceleration (a) is given by:
a = (m * g * sinθ - μ * m * g * cosθ) / m
where:
- m is the mass of Annie (55 kg)
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
- θ is the angle of inclination (25 degrees)
- μ is the coefficient of kinetic friction (0.15)
Substituting these values into the equation, we get:
a = (55 kg * 9.8 m/s^2 * sin(25 degrees) - 0.15 * 55 kg * 9.8 m/s^2 * cos(25 degrees)) / 55 kg
Solving this equation, you will find the value of acceleration (a) in meters per second squared (m/s^2).
Once you have the acceleration value, you can use the kinematic equation v = u + a * t to find Annie's velocity (v) after a given time (t). In this case, the initial velocity (u) is zero since she starts from rest. So, the equation becomes:
v = a * t
Substituting the value of acceleration (a) and time (t), you can find Annie's velocity (v) after 7 seconds.