Final answer:
The initial speed of the ball is 10.6 m/s and the maximum height reached by the ball is 5.71 m.
Step-by-step explanation:
To determine the initial speed of the ball, we can use the principle of conservation of energy. When the ball is at its highest point, its kinetic energy is zero, so all its initial energy is in the form of potential energy. The potential energy stored in the spring when it is compressed is given by:
PE = 0.5kx^2
where PE is the potential energy, k is the spring stiffness constant, and x is the compression distance. Plugging in the values: PE = 0.5 * 950 * (0.15)^2 = 16.875 J
The potential energy can be equated to the initial kinetic energy of the ball:
KE = 0.5mv^2
where KE is the kinetic energy, m is the mass of the ball, and v is its initial speed. Plugging in the values: 16.875 = 0.5 * 0.3 * v^2 => v^2 = 112.5 => v = 10.6 m/s
(a) The initial speed of the ball is 10.6 m/s.
(b) To determine the maximum height reached by the ball, we can use the conservation of mechanical energy. At the highest point, the kinetic energy is zero, so all the initial energy is in the form of potential energy. The maximum height can be found using the equation:
PE = mgh
where PE is the potential energy, m is the mass of the ball, g is the acceleration due to gravity, and h is the maximum height. Plugging in the values: 16.875 = 0.3 * 9.8 * h => h = 5.71 m
(b) The maximum height reached by the ball is 5.71 m.