How Do I Find the Speed Without Friction?

[max1020]

some children go tobogganing on an icy hill. They start from rest at the top of the hill as shown in the diagram. The toboggan and children have a combined mass of 90 kg. If friction is small enough to be ignored, determine:
The speed of the toboggan at B
A is at 10m
B is at 0
C is at 3m
I only know the potential energy for A, the mass, and initial velocity

 

[Nathanael]

I only know the potential energy for A, the mass, and initial velocity

You know the potential energy for A relative to where? Relative to B?

If so, then that's enough information.

You know about conservation of energy, right? All of the potential energy of A relative to B will have been converted into kinetic energy (at point B).

 

[max1020]

I know the total mechanical energy for A which is 8820J

 

[Nathanael]

That is the sum of the kinetic and gravitational potential energy at point A?

If so, then that sum will have the same value at point B.

 

[max1020]

But how do I use that to find speed? Is there a formula for that

 

[HallsofIvy]

Conservation of energy: the total of potential energy and kinetic energy is constant. You know the potential energy at the top where the kinetic energy is 0. At a lower point where the potential energy is lower, the kinetic energy is the difference between the two potential energies. You can find the velocity from the kinetic energy.

 

[NascentOxygen]

But how do I use that to find speed? Is there a formula for that

Do you know a formula that relates the K.E. of an object to its velocity?

 

[max1020]

Do you know a formula that relates the K.E. of an object to its velocity?

Is it
V=sqrt2k/m

 

[NascentOxygen]

Is it
V=sqrt2k/m

No, not quite right...but you could make it right be adding a pair of parentheses.