A rocket shoot straight up from the launch pad. Five seconds after lift off, an observer 2 miles away notes that the rocket's angle of elevation is 41 degrees. How far did the rocket rise during those 4 seconds?
Ignore that first reply, it was meant to go elsewhere.
I am assuming that the time of 4 seconds vs 5 seconds is a typo.
let the height be h miles
then tan 41 = h/2
h = 2tan41 = 1.74 miles
To find the distance the rocket rose during those 4 seconds, we need to understand the concept of trigonometry and use the angle of elevation.
First, let's draw a diagram to visualize the situation. Imagine a right triangle where the observer is at one corner, the vertical distance from the observer to the rocket is the height (h) we want to find, and the horizontal distance from the observer to the rocket is 2 miles. The angle of elevation, in this case, is 41 degrees.
|
|
h | 41°
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|___ 2 miles
Now, we can use the tangent function to find the height (h) of the rocket.
The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side. In this case, the opposite side is the height (h), and the adjacent side is the horizontal distance of 2 miles.
The tangent of 41 degrees can be written as:
tan(41°) = h / 2 miles
Now, to solve for h, we can multiply both sides of the equation by 2 miles:
h = 2 miles * tan(41°)
Using a calculator, we can find the value of tan(41°) ≈ 0.869:
h = 2 miles * 0.869
h ≈ 1.738 miles
Therefore, the rocket rose approximately 1.738 miles during those 4 seconds.
look at my solution to #2 question (I erroneously called it #1)
the question is identical in structure to yours.
See if you can follow it, then do yours.
oops the question was suppose to read a rocket shoots striaght up from the launch pad. Five seconds after lift off, an observer 2 miles away notes that the rocket's angle of elevation is 3.5 degrees. Four seconds after that, the angle of elevation is 41 degrees. How far did th erocket rise during those four seconds?
ok, simple !
Just repeat the above calculation for 3.5 degrees, the subtract the two answers.