How to Calculate Speed at Different Points Using Conservation of Energy?

[Peterson]

INTRODUCTION:
This is a problem from my Introduction to Physical Science class using "Conceptual Physics" 10th Ed.by Paul G. Hewitt

EXACT PROBLEM:
"The block in the figure at the right has a mass of 8kg and an initial speed of 7 m/s at Point A. Neglect frictional forces."

PROBLEMS FACED:
a) What will be its speed when it reaches Point B?
b) What will be its speed when it reaches Point C?

MY THOUGHTS:
Should I be looking for kinetic energy? What am I doing here?

 

[Peterson]

This is the diagram:

 

[teknodude]

Kinetic and Potential energy. Looks like an application of work energy/

 

[denverdoc]

I would think that speed is in this case equal to the initial plus any provided by external forces. In this case, the only other force is gravity. So as you suggest use th potential energy from gravity to add to the initial velocity. Whats that eqn?