Engineers have determined that the maximum safe speed around a
particular non-banked curve is 20 m/s. if the coefficient of friction
between the tires and the road is 0.703, what is the radius of the curve?

58.1 m

Explanation:

Draw a free body diagram of the vehicle.  There are three forces: normal force N pushing up, weight force mg pulling down, and friction force Nμ pushing towards the center of the circle.

Sum of forces in the y direction:

∑F = ma

N − mg = 0

N = mg

Sum of forces in the radial direction:

∑F = ma

Nμ = m v² / r

Substitute and solve for r:

mgμ = m v² / r

gμ = v² / r

r = v² / (gμ)

Plug in values:

r = (20 m/s)² / (9.8 m/s² × 0.703)

r = 58.1 m