A rocket is launched at an angle of ascent (elevation) of 18 degrees. When it has traveled 6000 ft, what is its height above the ground?
L = traveled way
H = Height
sin ( 18° ) = H / L
sin ( 18° ) = H / 6000
H = 6000 sin ( 18° )
H = 6000 0.30902
H = 1854.12 ft
There is insufficient information to determine the height after traveling 6000 ft. horizontally. It will definitely be on an angle less than 18º from the launch point.
To determine the height of the rocket above the ground, we can use trigonometry. Specifically, we need to use the tangent function since we know the angle of ascent and the horizontal distance traveled.
Step 1: Convert the angle from degrees to radians
The trigonometric functions in most programming languages, calculators, and mathematical libraries expect angles to be in radians. To convert from degrees to radians, we can use the formula:
radians = degrees * (π / 180)
Given that the angle of ascent is 18 degrees, we can calculate the angle in radians as:
angle_radians = 18 * (π / 180)
Step 2: Calculate the height above the ground
We can use the tangent function to find the height above the ground. The formula is:
height = horizontal_distance * tan(angle_radians)
Given that the horizontal distance traveled is 6000 ft, we can calculate the height as:
height = 6000 * tan(angle_radians)
Now, let's calculate the value of height using this formula.