Explanation:
Given formula:
ME=
mv²+mgh
To make height the subject of the formula, follow the following procedures;
Subtract
mv² from both side of equation
M.E -
mv² =
mv² -
mv²+mgh
This gives:
M.E -
mv² = mgh
Multiply both sides of the expression by 
( M.E -
mv² ) x
=
x mgh
h = ( M.E -
mv² ) x 
Learn more:
Kinetic energy brainly.com/question/6536722
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Answer:
See the answers below
Explanation:
To solve this problem we must use the following equation of kinematics.

where:
Vf = final velocity [m/s]
Vo = initial velocity [m/s]
a = acceleration [m/s²]
t = time [s]
<u>First case</u>
Vf = 6 [m/s]
Vo = 2 [m/s]
t = 2 [s]
![6=2+a*2\\4=2*a\\a=2[m/s^{2} ]](https://tex.z-dn.net/?f=6%3D2%2Ba%2A2%5C%5C4%3D2%2Aa%5C%5Ca%3D2%5Bm%2Fs%5E%7B2%7D%20%5D)
<u>Second case</u>
Vf = 25 [m/s]
Vo = 5 [m/s]
a = 2 [m/s²]
![25=5+2*t\\t = 10 [s]](https://tex.z-dn.net/?f=25%3D5%2B2%2At%5C%5Ct%20%3D%2010%20%5Bs%5D)
<u>Third case</u>
Vo =4 [m/s]
a = 10 [m/s²]
t = 2 [s]
![v_{f}=4+10*2\\v_{f}=24 [m/s]](https://tex.z-dn.net/?f=v_%7Bf%7D%3D4%2B10%2A2%5C%5Cv_%7Bf%7D%3D24%20%5Bm%2Fs%5D)
<u>Fourth Case</u>
Vf = final velocity [m/s]
Vo = initial velocity [m/s]
a = acceleration [m/s²]
t = time [s]
![v_{f}=5+8*10\\v_{f}=85 [m/s]](https://tex.z-dn.net/?f=v_%7Bf%7D%3D5%2B8%2A10%5C%5Cv_%7Bf%7D%3D85%20%5Bm%2Fs%5D)
<u>Fifth case</u>
Vf = final velocity [m/s]
Vo = initial velocity [m/s]
a = acceleration [m/s²]
t = time [s]

Answer:
6.88 m/s
Explanation:
The Conservation of Energy states that:
Initial Kinetic Energy + Initial Potential Energy = Final Kinetic Energy + Final Potential Energy
So we can write

We can cancel the common factor of
which leaves us with

Lets solve for 

Subtract
from both sides of the equation.

Multiply both sides of the equation by 2.

Simplify the left side.
Apply the distributive property.

Cancel the common factor of 2.

Take the square root of both sides of the equation to eliminate the exponent on the right side.

We are given
.
We can now solve for the final velocity.

Anything multiplied by 0 is 0.


