The period of a mass-spring system is:
T = 2π
T = period, m = mass, k = spring constant
Given values:
T = 8π s
k = 2 N/m
Plug in and solve for m:
8π = 2π
= 4
m/2 = 16
m = 32 kg
Choice A
As we know that here no air resistance while ball is moving in air
So here we will say that
initial total energy = final total energy

here we know that
(as it will be on ground at initial and final position)
so we will say

since mass is always conserved
so we will say that final speed of the ball must be equal to the initial speed of the ball
so we have

Sine value is defined in the following way
Explanation:
- In a right triangle, the sine of an angle is the length of the opposite side divided by the length of the hypotenuse. Try this Drag any vertex of the triangle and see how the sine of A and C are calculated. The sine function, along with cosine and tangent, is one of the three most common trigonometric functions.
- Let's start with the basic sine function, f (t) = sin(t). This function has an amplitude of 1 because the graph goes one unit up and one unit down from the midline of the graph. This function has a period of 2π because the sine wave repeats every 2π units.
- Trigonometric sine calculator.
Sine calculator
In order to calculate sin(x) on the calculator:
Enter the input angle.
Select angle type of degrees (°) or radians (rad) in the combo box.
Press the = button to calculate the result.
Answer:
a) 20.54 J
b) 30.97 J
c) 10.43 J
d) -20.54 J
Explanation:
m = Mass
g = Acceleration due to gravity = 9.81 m/s²
h = Height

Work done by the ball's weight is 20.54 J

Gravitational potential energy of the basketball, relative to the ground, when it is released is 30.97 J

Gravitational potential energy of the basketball, relative to the ground, when it is released is 10.43 J
Change in gravitational potential energy

Change in gravitational potential energy is given by -20.54 J