A mass of 2kg was thrown straight up with a speed of 15m/s. (a) find the initial KE (b) how high does the mass rise? (c) what is the GPE of the mass at the highest point?

To find the answers to these questions, we can use the principles of energy conservation. Let's break it down step by step:

(a) To find the initial kinetic energy (KE) of the mass, we can use the formula:

KE = 0.5 * m * v^2

Where:
m = mass of the object (2kg in this case)
v = velocity/speed of the object (15m/s in this case)

Substituting the values into the formula:

KE = 0.5 * 2kg * (15m/s)^2
KE = 0.5 * 2 * 225
KE = 225 J

So, the initial kinetic energy of the mass is 225 Joules.

(b) To determine how high the mass rises, we can use the principle of conservation of mechanical energy, which states that the sum of kinetic energy (KE) and gravitational potential energy (GPE) remains constant throughout the motion.

At the highest point, the mass comes to a momentary stop, which means the entire initial kinetic energy has been converted into gravitational potential energy.

Therefore, we can equate the initial kinetic energy to the gravitational potential energy at the highest point:

KE = GPE

Substituting the values:

225 J = m * g * h

Where:
m = mass of the object (2kg)
g = acceleration due to gravity (9.8 m/s^2)
h = height

Solving for h:

h = 225 J / (2kg * 9.8 m/s^2)
h = 11.5 m

So, the mass rises to a height of 11.5 meters.

(c) To calculate the gravitational potential energy (GPE) of the mass at the highest point, we can use the formula:

GPE = m * g * h

Substituting the values:

GPE = 2kg * 9.8 m/s^2 * 11.5m
GPE = 225.6 J

So, the gravitational potential energy of the mass at the highest point is approximately 225.6 Joules.