Explanation:
It is given that,
Spring constant of the spring, k = 15 N/m
Amplitude of the oscillation, A = 7.5 cm = 0.075 m
Number of oscillations, N = 31
Time, t = 15 s
(a) Let m is the mass of the ball. The frequency of oscillation of the spring is given by :

Total number of oscillation per unit time is called frequency of oscillation. Here, 


m = 0.0895 kg
or
m = 89 g
(b) The maximum speed of the ball that is given by :





Hence, this is the required solution.
Answer:
a) t = 0.528 s
b) D = 1.62 m
Explanation:
given,
speed of the baseball = 3.75 m/s
angle made with the horizontal = 35°
height of the roof edge = 2.5 m
using equation of motion



4.9 t² + 2.15 t - 2.5 = 0
on solving the above equation
t = 0.528 s
b) D = v cos θ × t
D = 3.75 × cos 35° ×0.528
D = 1.62 m
Answer: elastic potential energy = 20.27 J
Explanation:
Given that the
Mass M = 0.470 kg
Height h = 4.40 m
Spring constant K = 85 N/m
The maximum elastic potential will be equal to the maximum kinetic energy experienced by the block.
But according to conservative of energy, the maximum kinetic energy is equal to the maximum potential energy experienced by the block of mass M.
That is
K .E = P.E = mgh
Where g = 9.8m/s^2
Substitutes all the parameters into the formula
K.E = 0.470 × 9.8 × 4.4
K.E = 20.27 J
Where K.E = maximum elastic potential energy stored in the spring during the motion of the blocks after the collision which is 20.27J.