Respuesta :
Answer:
The speed of Sam at the bottom is 7.19 m/s.
Explanation:
Given that,
Mass of Sam = 79 kg
Height = 11 m
Length = 120 m
Coefficient of kinetic friction = 0.07
Suppose, an object of mass m is at rest at the top of a smooth slope of height h and length L. The coefficient of kinetic friction between the object and the surface, micro-kilometer , is small enough that the object will slide down the slope if given a very small push to get it started.
We need to calculate the speed at the bottom
Using conservation of energy
[tex]P.E=K.E+\text{energy lost of friction}[/tex]
[tex]mgh=\dfrac{1}{2}mv^2+\mu mg(\sqrt{L^2-h^2})[/tex]
[tex]v^2=2gh-2\mu g(\sqrt{L^2-h^2}[/tex]
[tex]v=\sqrt{2gh-2\mu g(\sqrt{L^2-h^2}}[/tex]
Where, m = mass
h = height
L= length
v = speed
g = acceleration due to gravity
Put the value into the formula
[tex]v=\sqrt{2\times9.8\times11-2\times0.07\times9.8(\sqrt{120^2-11^2})}[/tex]
[tex]v=7.19\ m/s[/tex]
Hence, The speed of Sam at the bottom is 7.19 m/s.
Velocity is the rate of change of position. Sam's velocity at the bottom of the slope with a height of 11 m is 13.8844 m/s.
What is velocity?
Velocity is the rate of change of position of an object with respect to time.
[tex]v = \dfrac{ds}{dt}[/tex]
We know that at the topmost height, the weight of Sam will act as potential energy, while during skiing down this potential energy will be partially converted to kinetic energy and part will be converted to heat or can say will be lost due to the friction, therefore,
Potential Energy = Kinetic energy + Energy loss due to the friction,
[tex]mgh = \frac{1}{2}mv^2 + \mu gh\sqrt{L^2+H^2}\\\\mgh - \mu gh\sqrt{L^2+H^2} = \frac{1}{2}mv^2\\\\2mgh - 2\mu gh\sqrt{L^2+H^2} = mv^2\\\\2gh(m - \mu \sqrt{L^2+H^2}) = mv^2\\\\v^2 = \dfrac{2gh}{m}(m - \mu \sqrt{L^2+H^2})[/tex]
Substitute the values,
Mass, m = 79 kg
Height, H = 11 m
Length, L = 120 m
Coefficient of kinetic friction, μ = 0.07
Acceleration due to gravity, g = 9.81 m/s²
[tex]v^2 = \dfrac{2 \times 9.81 \times 11}{79}[79-0.07\sqrt{120^2+11^2}]\\\\v^2 = 215.82 - 23.0442\\\\v = 13.8844\rm\ m/s[/tex]
Hence, Sam's velocity at the bottom of the slope with a height of 11 m is 13.8844 m/s.
Learn more about Velocity:
https://brainly.com/question/862972
