Answer:
24 m/s
Explanation:
Let's say that under very icy conditions, there is no friction.
Draw a free body diagram. There are 2 forces acting on the van. Gravity straight down, and normal force perpendicular to the surface.
Sum of the forces in the radial (+x) direction:
∑F = ma
N sin θ = m v² / r
Sum of the forces in the y direction:
∑F = ma
N cos θ − mg = 0
Solve for N in the second equation:
N cos θ = mg
N = mg / cos θ
Substitute into the first equation:
(mg / cos θ) sin θ = m v² / r
mg tan θ = m v² / r
g tan θ = v² / r
v = √(gr tan θ)
Given g = 9.8 m/s², r = 130 m, and θ = 24.8°:
v = √(9.8 m/s² × 130 m × tan 24.8°)
v = 24.3 m/s
Rounded to two significant figures, the maximum velocity is 24 m/s (approximately 54 mph).
