Answer:
h = 40 m
Explanation:
- Assuming no friction present, total mechanical energy must be conserved, so the following expression stands:
- ΔK + ΔU = 0 (1)
- Now, if the car is at rest at the crest of the hill, the change in kinetic energy is just as follows:
[tex]\Delta K = \frac{1}{2} * m* v_{b} ^{2}[/tex] (2)
where vb = speed at the bottom = 28 m/s
- If we define the bottom as our zero reference level for the gravitational potential energy, we can write the following equation:
[tex]\Delta U = U_{f} - U_{i} = 0- m*g*h = -m*g*h[/tex] (3)
- From (1) we get:
- ΔK = -ΔU
- Replacing by (2) and (3), we get:
[tex]\frac{1}{2} * m* v^{2} = m*g*h[/tex]
- Simplifying and rearranging terms, we can solve for h (height required) as follows:
[tex]h = \frac{v_{b} ^{2} }{2*g} = \frac{(28m/s)^{2}}{2*9.8m/s2} = 40 m[/tex]
