An apple with mass M is hanging at rest from the lower end of a light vertical rope. A dart of mass M/4 is shot vertically upward, strikes the bottom of the apple, and remains embedded in it.

The apple moves a height of  h = [tex]\frac{v^{2} }{50 g}[/tex] because of its collision with the dart. How do we calculate height?we can calculate the height of an object using the distance and angle.In order to calculate the height of an apple with mass M is hanging at rest from the lower end of a light vertical rope. A dart of mass M/4 is shot vertically upward, strikes the bottom of the apple, and remains embedded in it.We first calculate the velocity that the final mass gets once the collision takes place, in order to do this, we use momentum conservation. pi = Pf = (5/4)MvWe get the value for the velocity of the final mass, v , once the collision has been produced. Once we have pi, with this final velocity, we can calculate the final height that the mass will get, to do this we use energy conservation. An instant after the collision, the mass has kinetic energy, and we say that that is our altitude zero, but when the mass gets to its higher altitude, the kinetic energy is zero and the potential energy is different than zero, and we will write as follows:Ei = Ef =  (1/2) (5/4 M (V/5)²  =(5/4 M)g*hEquating and solving for height, we will get as the apple moves a height of  h = [tex]\frac{v^{2} }{50 g}[/tex] because of its collision with the dart. Learn more about height at: https://brainly.com/question/12446886#SPJ1