Asolid ball is at the top of a 2 m tall ramp. if it is given a push so that it’s initial speed is 1.75 m/s, what is it’s speed when it reaches the bottom of the ramp?

6.50m/s

Explanation:

Using conservation of energy, the total energy in the system is conserved. We know that the ball has potential energy initially because it is elevated 2 meters. We also know it has kinetic energy because it is given an initial speed of 1.75 m/s. At the bottom of the ramp, it loses all potential energy and is converted directly to kinetic energy. We can model the equation as below. U is the potential energy, K is the initial kinetic energy and K' is final kinetic energy.

Equation for kinetic energy is

and potential energy is:

Plug these equation to the first equation and simplify (v' is final speed):

Plug in the values:

Final speed is 6.50m/s

when two balls of the different masses are dropped from equal height, they reach the ground at the same time .this is because they experience the same acceleration.

the acceleration is independent of mass.

thus when they are dropped they will always maintain the same velocity and travel the same distance (neglect air resistance of course) at the same time.