Hlo anyone help a stone is thrown upward with the kinetic energy of 10 joule if it goes up to a maximum height of 5 M find the initial velocity and mass of the stone??
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Let's solve ~

As we know the total energy [P.E + K.E = C] of the system remains constant throughout the motion,

So, When a stone was thrown initially it didn't had any potential energy (P.E = 0) but had kinetic Energy of 10 joules.

So, total energy = P.E + K.E = 0 + 10 = 10 joules

As per the given information, equate it with the formula.

Now, As it approaches 5m height it comes to rest, Therefore velocity = 0. And since velocity = 0 then Kinetic Energy = 0

Now, let's find the Potential Energy at that point ~

And here, the Total energy = P.E + K.E = 10 Joules

So,

Therefore, mass of the object is 0.2 kg = 200 grams

Now, plug the value of mass (m) in the equation of kinetic Energy to find the initial velocity of the stone ~

Hence, velocity of the particle at the beginning was 10 m/s

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west