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The speed of an object at the height of (1/2)hmax can be determined using the conservation of energy principle. The total mechanical energy of the object is constant and is equal to the sum of its potential energy and kinetic energy.
At the height of (1/2)hmax, the object has potential energy equal to:
PE = mgh/2
where m is the mass of the object, g is the acceleration due to gravity, and h is the maximum height reached by the object.
At this height, the object has converted half of its potential energy into kinetic energy, so the kinetic energy is:
KE = mgu^2/2
where u is the speed of the object at the height of (1/2)hmax.
Since the total energy is constant, we can equate the potential and kinetic energy equations:
mgh/2 = mgu^2/2
Simplifying and solving for u:
u^2 = gh
u = sqrt(gh)
Therefore, the speed u of the object at the height of (1/2)hmax is equal to the square root of the product of the acceleration due to gravity and the hei
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