Answer:
The time constant is
Explanation:
From the question we are told that
The spring constant is 
The mass of the ball is 
The amplitude of the oscillation t the beginning is 
The amplitude after time t is 
The number of oscillation is 
Generally the time taken to attain the second amplitude is mathematically represented as
Here T is the period of oscillation

=> 
=> 
Generally the amplitude at time t is mathematically represented as

Here a is the damping constant so
at
, 
So

=> 
taking natural log of both sides
=>
=> 
Generally the time constant is mathematically represented as
=>
=>
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:



Answer:
Stretch can be obtained using the Elastic potential energy formula.
The expression to find the stretch (x) is 
Explanation:
Given:
Elastic potential energy (EPE) of the spring mass system and the spring constant (k) are given.
To find: Elongation in the spring (x).
We can find the elongation or stretch of the spring using the formula for Elastic Potential Energy (EPE).
The formula to find EPE is given as:

Rewriting the above expression in terms of 'x', we get:

Example:
If EPE = 100 J and spring constant, k = 2 N/m.
Elongation or stretch is given as:

Therefore, the stretch in the spring is 10 m.
So, stretch in the spring can be calculated using the formula for Elastic Potential Energy.
Answer:
The distance traveled in 1 year is:
Explanation:
Given
--- speed
--- time
Required
The distance traveled
This is calculated as:

So, we have:

This gives:


-- approximated
Answer:
304 meters downstream
Explanation:
The given parameters are;
The speed of the swimmer = 2.00 m/s
The width of the river = 73.0 m
The speed of the river = 8.00 m/s
Therefore;
The direction of the swimmer's resultant velocity = tan⁻¹(8/2) ≈ 75.96° downstream
The distance downstream the swimmer will reach the opposite shore = 4 × 73 = 304 m downstream
The distance downstream the swimmer will reach the opposite shore = 304 m downstream