In the first case, the force acting on the spring is the weight of the mass:

This force causes a stretching of

on the spring, so we can use these data to find the spring constant:

In the second case, the first mass is replaced with a second mass, whose weight is

And since we know the spring constant, we can calculate the new elongation of the spring:
Let height of twin falls = x
height of seven falls = 2.5x
x + 2.5x = 420
3.5x = 420
x = 420/3.5 = 120
so twin falls = x = 120 ft
seven falls = 2.5x = 300 ft
To solve this problem it is necessary to apply the concepts related to frequency as a function of speed and wavelength as well as the kinematic equations of simple harmonic motion
From the definition we know that the frequency can be expressed as

Where,


Therefore the frequency would be given as


The frequency is directly proportional to the angular velocity therefore



Now the maximum speed from the simple harmonic movement is given by

Where
A = Amplitude
Then replacing,


Therefore the maximum speed of a point on the string is 3.59m/s
Answer:
14.85 m/s
Explanation:
From the question given above, the following data were obtained:
Height (h) of tower = 45 m
Horizontal distance (s) moved by the balloon = 45 m
Horizontal velocity (u) =?
Next, we shall determine the time taken for the balloon to hit the shoe of the passerby. This is illustrated below:
Height (h) of tower = 45 m
Acceleration due to gravity (g) = 9.8 m/s²
Time (t) =?
h = ½gt²
45 = ½ × 9.8 × t²
45 = 4.8 × t²
Divide both side by 4.9
t² = 45/4.9
Take the square root of both side
t = √(45/4.9)
t = 3.03 s
Finally, we shall determine the magnitude of the horizontal velocity of the balloon as shown below:
Horizontal distance (s) moved by the balloon = 45 m
Time (t) = 3.03 s
Horizontal velocity (u) =?
s = ut
45 = u × 3.03
Divide both side by 3.03
u = 45/3.03
u = 14.85 m/s
Thus, the magnitude of the horizontal velocity of the balloon was 14.85 m/s
The longitude based on the time difference is 15 degrees.
<h3>Longitude of complete rotation of the Earth</h3>
The longitude of a complete rotation of the earth in a 24 hours is calculated as follows;

<h3>Time difference</h3>
The time difference between the local apparent solar time and the Greenwich time is calculated as follows;

Since it is one hour time difference, the longitude is 15 degrees.
Learn more about Earth longitude here: brainly.com/question/1939015