Final answer:
The speed along the descent path is 63.1 m/s and the angle with the vertical is 28 degrees.
Step-by-step explanation:
The speed at which the vehicle moves along its descent path can be found using the Pythagorean theorem. The horizontal velocity and vertical velocity form the two sides of a right triangle, with the descent path being the hypotenuse. Using the equation a^2 + b^2 = c^2, we can calculate the speed as:
Speed = sqrt((horizontal velocity)^2 + (vertical velocity)^2)
Plugging in the given values, we get:
Speed = sqrt((55.6 m/s)^2 + (29.1 m/s)^2) = 63.1 m/s
The speed at which the vehicle moves along its descent path is 63.1 m/s.
To find the angle with the vertical, we can use trigonometry. The angle can be found using the equation tan(theta) = opposite/adjacent, where the opposite side is the vertical velocity and the adjacent side is the horizontal velocity. Rearranging the equation, we get:
tan(theta) = vertical velocity/horizontal velocity
Plugging in the given values, we get:
tan(theta) = 29.1 m/s / 55.6 m/s = 0.523
Taking the inverse tangent of 0.523, we get:
theta = arctan(0.523) = 28 degrees
The angle with the vertical is 28 degrees.