The time taken by the pulse to travel from one support to the other is 0.208 s.
<h3>Given:</h3>The mass of the cord is m = 0.65 kg.
The distance between the supports is, d = 8.0 m.
The tension in the cord is T = 120 N.
The time taken by the pulse to travel from one support to the other is given as,
Here, v is the linear velocity of a pulse. Its value is,
Then,
Thus, the time taken by the pulse to travel from one support to the other is 0.208 s.
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Answer:
The angle of elevation of the rocket is increasing at a rate of 48.780º per second.
Explanation:
Geometrically speaking, the distance between the rocket and the observer (), measured in kilometers, can be represented by a right triangle:
(1)
Where:
- Horizontal distance between the rocket and the observer, measured in kilometers.
- Vertical distance between the rocket and the observer, measured in kilometers.
The angle of elevation of the rocket (), measured in sexagesimal degrees, is defined by the following trigonometric relation:
(2)
If we know that , then the expression is:
And the rate of change of this angle is determined by derivatives:
Where:
- Rate of change of the angle of elevation, measured in sexagesimal degrees.
- Vertical speed of the rocket, measured in kilometers per hour.
If we know that and
, then the rate of change of the angle of elevation is:
The angle of elevation of the rocket is increasing at a rate of 48.780º per second.