(Originais Teachy 2023) - Question Medium of Physics

A high school student decides to build a projectile launcher using a spring. He attaches the spring to the fixed end of his launcher and compresses the spring to a certain distance to store elastic potential energy. When the spring is compressed, its force follows Hooke's Law, which relates the elastic force (-kx) to the spring's elastic coefficient (k) and the distance (x) it is compressed relative to its natural length. a) If the spring's elastic coefficient is 50 N/m and the student compresses the spring by 0.20 m, what is the work done by the elastic force when compressing the spring? b) Suppose all the elastic potential energy stored in the spring is converted into kinetic energy of the projectile when the spring is released. If the mass of the launched projectile is 0.1 kg, determine the velocity of the projectile as soon as it leaves the launcher. c) Consider the launcher to be pointing horizontally and the height of the launcher relative to the ground to be 1.5 m. Using the velocity found in part b, determine the horizontal range of the projectile when it hits the ground. Disregard air resistance.