Answer:
travel time is 7.58 s
Explanation:
We must know the acceleration of the sled and the girl, for this we must use Newton's second law
F = m a
Since this is a vector equation, let's separate it into its xy components, the best selection of the coordinate system is the X axis parallel to the plane and the Y axis perpendicular to it.
In the attached you can see a free body diagram of this situation, let's write Newton's equations on each axis
X axis
Wx + F - fr = m a (1)
Axis y
N- Wy = 0
N = Wy
Let's use trigonometry to find the weight components
Wx = W sin θ
Wy = W cos θ
In addition, the formula for friction force is
fr = n N
Let's clear the acceleration of equation 1
a = (W sin θ + F - m N) / m
a = (mg sin θ + F - m mg cos θ) / m
a = g (sin θ -m cos θ) + F / m
Let's replace and calculate
a = 9.8 (sin 30 - 0.299 cos 30) + 148 / 75.7
a = 2.36 + 1.96
a = 4,317 m / s²
We already have the acceleration, the speed is zero to leave the rest (Vo = 0) and give the length that runs 124 m, let's use the kinematic equations
x = v₀ t + ½ a t²
x = ½ a t²
t² = 2x / a
t = √ 2x / a
Let's calculate
t = √( 2 124 / 4,317) = √ 57.45
t = 7.58 s
