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.