mass of the bottle in each case is M = 0.250 kg
now as per given speeds we can use the formula of kinetic energy to find it
1) when speed is 2 m/s
kinetic energy is given as


2) when speed is 3 m/s
kinetic energy is given as


3) when speed is 4 m/s
kinetic energy is given as


4) when speed is 5 m/s
kinetic energy is given as


5) when speed is 6 m/s
kinetic energy is given as


Actually what the problem meant about the westward
component of the ball’s displacement is the horizontal component of the
displacement. To help us better understand the problem, I attached a figure of
the situation.
We can see from the figure that to solve for the value of
the horizontal component, we have to make use of the sin function. That is:
sin θ = side opposite to the angle / hypotenuse of the
triangle
sin 42 = x / 40 m
x = (40 m) sin 42
x = 26.77 m
Therefore the ball has a westward
displacement of about 26.77 m
Answer:
(a) work required to lift the object is 1029 J
(b) the gravitational potential energy gained by this object is 1029 J
Explanation:
Given;
mass of the object, m = 35 kg
height through which the object was lifted, h = 3 m
(a) work required to lift the object
W = F x d
W = (mg) x h
W = 35 x 9.8 x 3
W = 1029 J
(b) the gravitational potential energy gained by this object is calculated as;
ΔP.E = Pf - Pi
where;
Pi is the initial gravitational potential energy, at initial height (hi = 0)
ΔP.E = (35 x 9.8 x 3) - (35 x 9.8 x 0)
ΔP.E = 1029 J
Refer to the diagram shown below.
The force, F, is applied at 5 cm from the elbow.
For dynamic equilibrium, the sum of moments about the elbow is zero.
Take moments about the elbow.
(5 cm)*(F N) - (30 cm)*(250 N) = 0
F = (30*250)/5 = 1500 N
Answer: 1500 N