Final answer:
The maximum safe speed at the top of a hill with a radius of 60m is calculated using the relationship between centripetal force and gravitational force, resulting in a maximum speed of 24.26 m/s.
Step-by-step explanation:
To determine the maximum speed a car can have without losing contact with the road at the top of a hill, one can use the concept of centripetal force and its relationship with gravitational force. At the very maximum speed, the centripetal force required to keep the car following the circular path of the hill's top would equal the gravitational force. Centripetal force (Fc) is defined as Fc = mv²/r, where m is the mass of the car, v is the velocity of the car, and r is the radius of the circular path (which is the hill in this case). Gravitational force (Fg) is defined as Fg = mg, where g is the acceleration due to gravity (9.81 m/s²). At the top of the hill, assuming the car is just at the verge of losing contact with the ground, Fc = Fg.
Setting the two forces equal gives us:
mv²/r = mg
Dividing both sides by m and solving for v we get:
v = √(rg)
Plugging in the values for r (60 m) and g (9.81 m/s²), we find the maximum safe speed v.
v = √(60 m * 9.81 m/s²)
v = √(588.6 m²/s²)
v = 24.26 m/s
Therefore, the maximum safe speed is 24.26 m/s.