# Suppose a roller-coaster car starts at a height of 39 m with a speed of 2.51 m/s. What will its...

## Question:

Suppose a roller-coaster car starts at a height of 39 m with a speed of 2.51 m/s. What will its speed be at height = 0 m if the average force of friction is equal to 0.22 times its weight? The total distance traveled is 53 m.

## Conservation Of Energy :

From the conservation of energy, the energy at one point can be converted into other forms depending upon the change that it possesses for example when a body having some potential energy is given a push then all the potential energy will be converted into kinetic energy.

Given

For the initial kinetic energy of the body:

{eq}K.E_i=\frac{1}{2}mu^2 {/eq}

For the final kinetic energy :

{eq}K.E_f=\frac{1}{2}mv^2 {/eq}

Now for the potential energy :

{eq}P.E= mgh {/eq}

Distance travlled when fritcion losses occur is :

{eq}S=53-39\\ S=14\ m {/eq}

From the conservation of energy:

{eq}P.E+K.E_i=K.E_f+F.E\\ mgh+\frac{1}{2}mu^2=\frac{1}{2}mv^2+(0.22\times m\times g\times S)\\ 9.81\times 39+\frac{1}{2}(2.51)^2=\frac{1}{2}v^2+(0.22\times 9.81\times 14)\\ 382.59+3.15=0.5v^2+30.21\\ v=26.66\ m/s {/eq}

Thus, the speed after every loss is 26.66 m 