A toy gun shoots spherical plastic projectiles by means of a spring. A typical projectil...

A toy gun shoots spherical plastic projectiles by means of a spring. A typical projectile has mass m = 25 g. The spring used has spring constant k = 15 N/m, and when put under load, it is displaced an amount as shown in Figure P6.90. The barrel of the gun exerts a slight frictional force of magnitude on the pellet as it moves down the barrel from its starting point a total length L = 15 cm. If the toy gun is fi red in a horizontal position, (a) at what position measured from the starting point does the pellet reach maximum velocity? Hint: Consider an equilibrium condition between the spring force and the friction force on the pellet before it leaves the spring. (b) What is the maximum speed achieved by the pellet as it is fi red from the gun? (c) At what speed does the pellet leave the barrel?