Suppose a daredevil attempted to jump a canyon, using a special rocket built for the stunt. Suppose it was launched off a ramp shown in the picture. The ramp was 325 feet in length and rose vertically 225 feet.
(a) Calculate the measure of the angle of elevation that the ramp makes with the ground.
b) The horizontal crossbeam is located halfway to the top of the ramp. Calculate the length of this crossbeam.
(a) tanθ = 225/325
(b) Assuming it was attached to vertical support from the end of the ramp, it would be
1/2 * 325 cosθ
or, 1/2 √(325^2-225^2)
the length of the ramp is the hypotenuse
(a) sin(Θ) = 225/325
scott got it right. My bad.
To find the angle of elevation that the ramp makes with the ground, we can use the inverse tangent function. The tangent of an angle is defined as the ratio of the opposite side to the adjacent side in a right triangle. In this case, the opposite side is the vertical rise of the ramp (225 feet), and the adjacent side is the horizontal distance of the ramp (325 feet).
(a) Calculating the angle of elevation:
tan θ = opposite/adjacent
tan θ = 225/325
θ = arctan(225/325)
You can use a scientific calculator or an online trigonometric calculator to find the value of arctan(225/325). This will give you the angle of elevation in degrees.
(b) To find the length of the horizontal crossbeam, we need to determine the height of the vertical rise that is halfway up the ramp. Since the ramp rises vertically 225 feet, the halfway point would be 225/2 = 112.5 feet.
We can now use the Pythagorean theorem to find the length of the horizontal crossbeam. The hypotenuse of the right triangle formed by the vertical rise (112.5 feet), the horizontal distance (325 feet), and the length of the crossbeam is the crossbeam itself.
Using the Pythagorean theorem:
a^2 + b^2 = c^2
Where a = 112.5 feet (vertical rise) and b = the length of the crossbeam (unknown).
Solving for b:
112.5^2 + b^2 = 325^2
b^2 = 325^2 - 112.5^2
b = √(325^2 - 112.5^2)
You can use a calculator to find the square root of (325^2 - 112.5^2). This will give you the length of the horizontal crossbeam.