a car traveling at 30 m/s loses a tire. the tire rolls to a hill which it begins climbing without slipping how high up the hill will the tire climb?

Kinetic energy at bottom = potential energy at top

(1/2) m v^2 + (1/2)I w^2 = m g h

but w = v/r
(1/2) m v^2 + (1/2)I v^2/r^2 = m g h
v^2 (m + I/r^2) = 2 m g h

You must know something about radius and moment of inertia to get answer.

omg thank you i forgot about kinetic energy and potential energy

To determine how high up the hill the tire will climb, we need to consider a few key concepts.

Firstly, we need to determine the initial velocity of the tire as it rolls up the hill. Since the tire loses contact with the car traveling at 30 m/s, it will initially have the same velocity. Therefore, the initial velocity of the tire is 30 m/s.

Next, we need to consider the conservation of mechanical energy. As the tire rolls up the hill, it will convert its initial kinetic energy to potential energy, gaining height in the process. We can use the following equation to calculate the height:

mgh = (1/2)mv^2

Where:
m is the mass of the tire (which we can assume to be constant)
g is the acceleration due to gravity (approximately 9.8 m/s^2)
h is the height we want to find
v is the velocity of the tire at that height, which we know is 30 m/s

Simplifying the equation, we have:

gh = (1/2)v^2

Now we can solve for h:

h = ((1/2)v^2) / g

Plugging in the values, we get:

h = ((1/2)(30^2)) / 9.8

Calculating this, we find:

h ≈ 45.92 meters

Therefore, the tire will climb approximately 45.92 meters up the hill.