Jessica attains a height of 4.7 feet above the launch and landing ramps after 1 second. Her initial velocity is 25 feet per second. To find the angle of her launch, which equation can you use with the given information to solve for θ? (Answer: 1 or 2).
Use the equation you selected to find Jessica's angle, θ. Substitute the known values and solve for θ. What is θ to the nearest tenth of a degree? (Enter only the number.)
sin theta = 4.7/25
so
theta = sin^-1 (4.7/25)
10.8 degrees
To solve for the angle θ, we can use the following equation:
θ = tan^(-1)((h - y) / x)
where:
- θ is the angle of launch
- h is the height obtained above the launch and landing ramps (4.7 feet in this case)
- y is the height of the launch ramp (assumed to be 0 feet in this case)
- x is the horizontal distance covered (1 second * 25 feet/second = 25 feet in this case)
Substituting the known values into the equation:
θ = tan^(-1)((4.7 - 0) / 25)
Let's calculate θ:
θ = tan^(-1)(4.7 / 25)
Using a calculator to find the inverse tangent, we get:
θ ≈ 10.8 degrees
So, to the nearest tenth of a degree, the angle θ is approximately 10.8 degrees.