𝑡= √ 2⋅𝑏 / g⋅sin(Θ)⋅cos(Θ) where b(length of base in feet) and g = 32.2 feet per second (acceleration of gravity). How long does is take to slide down with a base of 12 feet at an angle of 440?

Answer 1

To determine the time it takes to slide down a base of 12 feet at an angle of 440 degrees, we'll use the given formula:

𝑡 = √(2⋅𝑏 / 𝑔⋅sin(Θ)⋅cos(Θ))

Given:

b (length of base) = 12 feet

g (acceleration of gravity) = 32.2 feet per second

Θ (angle) = 440 degrees

First, we need to convert the angle from degrees to radians since the trigonometric functions in the formula expect angles in radians. The conversion formula is:

radians = degrees × π / 180

Converting 440 degrees to radians:

Θ (radians) = 440 × π / 180

Θ (radians) ≈ 7.6394

Now we can substitute the values into the formula:

𝑡 = √(2⋅12 / 32.2⋅sin(7.6394)⋅cos(7.6394))

Calculating this expression:

𝑡 = √(24 / (32.2⋅sin(7.6394)⋅cos(7.6394)))

𝑡 ≈ √(24 / (32.2⋅0.134⋅0.991))

𝑡 ≈ √(24 / (32.2⋅0.132794⋅0.991))

𝑡 ≈ √(24 / 4.238)

𝑡 ≈ √5.668

𝑡 ≈ 2.38 seconds (approximately)

Therefore, it takes approximately 2.38 seconds to slide down with a base of 12 feet at an angle of 440 degrees.