Answer:
9.35 m/s^2
n = 292.24
Explanation:
y = 0.2×(x^2) , the equation that desribes the slope is parabolic, then;
the tangent line at a point can be found by differentiating the equation:
dy/dx = 0.4×x
then, at x = 8 m:
dy/dx = 0.4×8 = 3.2
that represents the slope of the tangent line
then to find the incline:
tan(∅) = 3.2
∅ = 72.65°
at the point, the toboggan is sitting at 72.65° on the incline.
since the surface is smooth, no friction.
the only force playing is the parallel component of gravity, then by Newton's second law:
F = m×a
a = F/m
= m×g×sin(∅)/m
= g×sin(∅)
= (9.8)×(sin(72.65°))
= 9.35 m/s^2
then the normal force is given by:
n = m×g×cos(∅) = (100)×(9.8)×(cos(72.65))
n = 292.24
