Explanation:
a. The velocity of the wind as a vector in component form will be represented as v vector:

b.The velocity of the jet relative to the air as a vector in component form will be represented as u vector

c. The true velocity of the jet as a vector will be represented as w:


d. The true speed of the jet will be calculated as:




e. The direction of the jet will be:



The period will be the same if the amplitude of the motion is increased to 2a
What is an Amplitude?
Amplitude refers to the maximum extent of a vibration or oscillation, measured from the position of equilibrium.
Here,
mass m is attached to the spring.
mass attached = m
time period = t
We know that,
The time period for the spring is calculated with the equation:

Where k is the spring constant
Now if the amplitude is doubled, it means that the distance from the equilibrium position to the displacement is doubled.
From the equation, we can say,
Time period of the spring is independent of the amplitude.
Hence,
Increasing the amplitude does not affect the period of the mass and spring system.
Learn more about time period here:
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Answer:
sin 2θ = 1 θ=45
Explanation:
They ask us to prove that the optimal launch angle is 45º, for this by reviewing the parabolic launch equations we have the scope equation
R = Vo² sin 2θ / g
Where R is the horizontal range, Vo is the initial velocity, g the acceleration of gravity and θ the launch angle. From this equation we see that the sine function is maximum 2θ = 90 since sin 90 = 1 which implies that θ = 45º; This proves that this is the optimum angle to have the maximum range.
We calculate the distance traveled for different angle
R = vo² Sin (2 15) /9.8
R = Vo² 0.051 m
In the table are all values in two ways
Angle (θ) distance R (x)
0 0 0
15 0.051 Vo² 0.5 Vo²/g
30 0.088 vo² 0.866 Vo²/g
45 0.102 Vo² 1 Vo²/g
60 0.088 Vo² 0.866 Vo²/g
75 0.051 vo² 0.5 Vo²/g
90 0 0
See graphic ( R Vs θ) in the attached ¡, it can be done with any program, for example EXCEL