Answer:
The maximum height could be 10.6 meters.
Explanation:
For this kind of exercise, we use the general principle for conservation of mechanical energy (E) that states:
[tex]E_1+W_f=E_2 [/tex] (1)
That means the mechanical energy an object has on a point 2 should be equal to the mechanical energy on a point 1 plus the energy transformed into heat due friction denoted as Wf (It is negative because is lost). In our case point 1 is the point where the roller coaster begins and point 2 is at the second hill. Tola mechanical energy is the sum of potential gravitational energy and kinetic energy, so (1) is :
[tex] K_{1}+U_{1}+W_{f}=K_{2}+U_{2}[/tex]
with K the kinetic energy and U the potential energy, remember potential energy is mgh and kinetic energy is [tex] \frac{mv^2}{2}[/tex] with m the mass, v the velocity and h the height, then:
[tex] \frac{mv_1^2}{2}+mgh_1+W_{f}=\frac{mv_2^2}{2}+mgh_2[/tex]
Solving for h_2:
[tex]h_2=\frac{\frac{mv_1^2}{2}+mgh_1+W_{f}-\frac{mv_2^2}{2}}{mg}=\frac{\frac{(1000)(6)^2}{2}+(1000)(9.8)(10)-1700-\frac{(1000)(4.6)^2}{2}}{(1000)(9.81)} [/tex]
[tex] h_2=10.6 m [/tex]
