A2-kg object is thrown vertically upward with an initial kinetic energy of 400 joules. to what height will the object rise?

At "20.38 m" height, the object will be rise. A further explanation is below..

Given:

Initial Kinetic energy,

400 J

Mass,

2 kg

As we know the formula,

→

→              

                 

                 

hence,

→

   

   

               

                 

Thus the above answer is right.

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Initial kinetic energy = 400J,
initial kinetic energy = [mass * Velocity²]/2 = [m * V²]/2,
[2 * V²]/2 = 400, V² = 400, V = √400 = 20 m/sec,
this V is initial velocity of object & it will keep on decreasing due to opposing gravitational force. At one point this will become zero & after that object will start to fall downward. If h is the maximum height it can reach, g is acceleration due to gravity & Vf if final velocity, then we can write, 
Vf² - V² = -2*g*h, ( -ve sign because gravity acts downward)
0 - (20²) = -2*9.81*h, 19.62*h = 400, 
h = 400/19.62 = 20.38m.

The purpose of a lab is to do your "expirements" the importance of the topic is so you can now what the story is about and the last one is because no one is me with my question ( what is 3 over 4 x - 9 = 27 maybe you can )