Respuesta :
Answer:
θ = 13.3º
Explanation:
To solve the problem let's use Newton's law, let's start by defining the coordinate system, the x-axis is parallel to the hill (plane) and the y-axis is perpendicular. In this system we must break down the weight
sin θ = Wx / W
cos θ = Wy / W
Wx = W sinT
Wy = W sinT
We write Newton's equation
X axis
Wx-fr = m a
Y Axis
N-Wy = 0
N = Wy = mg cosT
Calculous la acceleration with cinematic
vf² = v₀² + 2 a x
a = (vf²-v₀²) / 2x
a = (4² - 1) / 2 25
a = 0.30 m / s²
They indicate that the friction force is 1/5 of the weight of the sled + child
fr = 1/5 W
We calculate
W sin θ -1/5 W = m a
mg (sin θ -1/5) = ma
sin θ = a / g + 1/5
sin θ = 0.30 / 9.8 + 1/5
θ = sin-1 (0.2306)
θ = 13.3º
The angle that the hill makes with the horizontal, on which the child slides down a snow-covered slope on a sled is 13.308 degrees.
What is work energy theorem?
According to the work energy theorem, the sum of all the forces acting on a body to do a work is equal to the change in the kinetic energy of the body.
It can be written as,
[tex]W=KE\\[/tex]
A child slides down a snow-covered slope on a sled. At the top of the hill, her mother gives her a push to start her off with a speed of 1.00 m/s.
The force due to gravity along the inclined plane is given as,
[tex]F=mg\sin\theta[/tex]
The frictional force acting on the sled is one-fifth of the combined weight of the child and the sled. Thus,
[tex]F_f=\dfrac{W}{5}\\F_f=\dfrac{mg}{5}[/tex]
The total work done,
[tex]W=mg\sin\theta-\dfrac{mg}{5}[/tex]
Change in kinetic energy,
[tex]\Delta KE=\dfrac{1}{2}mv^2-\dfrac{1}{2}mu^2[/tex]
By the work-energy theorem,
[tex](mg\sin\theta-\dfrac{mg}{5})s=\dfrac{1}{2}mv^2-\dfrac{1}{2}mu^2[/tex]
The child travels for a distance of 25.0 m and her speed at the bottom is 4.00 m/s .Thus, plug in the values as,
[tex][(9.8)\sin\theta-\dfrac{(9.8)}{5}](25)=\dfrac{1}{2}(4)^2-\dfrac{1}{2}(1.1)^2\\\sin\theta=0.2302\\\theta=13.308^o[/tex]
Thus, the angle that the hill makes with the horizontal, on which the child slides down a snow-covered slope on a sled is 13.308 degrees.
Learn more about the work energy theorem here;
https://brainly.com/question/22236101
