I assume that is 5.5 m/s, the initial velocity.
Ok, assuming that, then you know the initial KEnergy; 1/2 .62 (5.5)^2 joules.
At the max height, the KE you are given is KE from horizontal motion. So subtract that amount (2.3J) from the initial KE, and you have then the KE that can go into vertical motion. From that, it is easy:
KE available for vertical motion=PE at top, where PEnergy at the top is mass*g*height and you solve for height.
In answering a question such as this one... you have the total PE = 7.1 J ..
Do you then divide this by mass 0.62 kg multiplied by 9.8 ms or by 9.8 squared ??? If it is 9.8 squared why is this so ????
Why does this mass have KE at top ??? should this not be 0 (zero) ???
Just a little confused...
Thanks
Fred
If you know the increase in PE, having derived if from the KE available from vertical motion, then divide PE by m*g to get the height increase. Joules divided by (kg m/s^2) equals meters
Thank you
To solve this problem, you will need to use the concepts of kinetic energy (KE), potential energy (PE), and gravity.
Let's break down the steps to find the answer:
1. Calculate the initial kinetic energy (KEi) using the given initial velocity of 5.5 m/s and the mass of 0.62 kg:
KEi = 1/2 * (0.62 kg) * (5.5 m/s)^2
2. Subtract the given KE of 2.3 J (from horizontal motion) from the initial kinetic energy to find the kinetic energy available for vertical motion (KEv):
KEv = KEi - 2.3 J
3. The kinetic energy available for vertical motion is equal to the potential energy at the maximum height (PE). Therefore, set KEv equal to PE:
PE = KEv
4. Rearrange the equation to solve for the height (h):
PE = m * g * h
h = PE / (m * g)
5. Substitute the given total potential energy of 7.1 J and the values for mass (0.62 kg) and gravitational acceleration (9.8 m/s^2):
h = 7.1 J / (0.62 kg * 9.8 m/s^2)
The resulting value of h will give you the height increase.
In response to your additional questions:
The division should be by the product of mass (0.62 kg) and gravitational acceleration (9.8 m/s^2). So, it should be divided by 0.62 kg * 9.8 m/s^2.
The mass has kinetic energy at the top because part of the initial kinetic energy is still available for vertical motion. The object is still moving horizontally when it reaches the top, so the remaining kinetic energy can be converted into vertical potential energy. The mass itself doesn't determine the kinetic energy; it depends on the initial velocity.
I hope this explanation helps clarify the steps and reasoning behind them. Let me know if you have any further questions!