Final answer:
To determine the speed of a 0.40 kg snowball at two thirds of its maximum height, with an initial kinetic energy of 150 J, conservation of mechanical energy can be used. First, calculate the potential energy at the desired height, then solve for the remaining kinetic energy, and finally determine the speed from this kinetic energy using the kinetic energy formula.
Step-by-step explanation:
The question involves finding the speed of the snowball when it is two thirds of the distance to its maximum height. Because energy is conserved, the total mechanical energy at the starting point must equal the total mechanical energy at the two-thirds height point. Initially, the snowball has only kinetic energy, which is given as 150 J.
To find the speed at the two-thirds height point, we first calculate the potential energy at this point, then use the conservation of mechanical energy to determine the remaining kinetic energy, and finally, use the kinetic energy to find the speed of the snowball.
Let Ei be the initial total mechanical energy, Ek be the kinetic energy, Ep be the potential energy, and v be the velocity of the snowball. The potential energy at the two-thirds height can be found using the formula Ep = mgh, where m is the mass of the snowball, g is the acceleration due to gravity (9.8 m/s2), and h is the height. However, since we don't have the explicit height value, we only know that at maximum height, all kinetic energy is converted to potential energy. At two-thirds height, some kinetic energy remains.
Using energy conservation: Ei = Ek (at two-thirds height) + Ep (at two-thirds height). We know that Ei is 150 J, and we can solve for Ek at two-thirds height. Finally, we can find the speed by rearranging the kinetic energy formula Ek = 0.5 * m * v2 to v = sqrt(2 * Ek / m).