Answer to Question #128089 in Mechanics | Relativity for john

Question #128089

A 50 g rock is launched vertically in the air by a slingshot. The slingshot exerts an average force of 53 N on the rock over a distance of 0.750 m.  

  1. Find the maximum height reached by the rock in [m].
  2. Find the speed of the rock as it leaves the slingshot in [m/s]?
Expert's answer

We can calculate the total energy given by the slingshot to the rock in form of "E = \\bar{F}\\cdot S = 53\\,\\mathrm{N}\\cdot 0.750\\,\\mathrm{m} = 39.75\\,\\mathrm{J}."

2. This energy transforms into the kinetic energy of the rock, so the initial velocity can be calculated as "v = \\sqrt{\\dfrac{2E}{m}} = 39.9\\,\\mathrm{m\/s}."

1. The rock stops to rise when the kinetic energy turns to 0. So the final potential energy is equal to the initial kinetic energy. Therefore,

"mgh = \\dfrac{mv^2}{2} = E, \\;\\; h = \\dfrac{E}{mg} \\approx 81\\,\\mathrm{m}."

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