Question

A descent vehicle landing on the moon has

a vertical velocity toward the surface of the
moon of 29.1 m/s. At the same time, it has a
horizontal velocity of 55.6 m/s.
At what speed does the vehicle move along
its descent path?
Answer in units of m/s.

009 (part 2 of 2)
At what angle with the vertical is its path?
Answer in units of ◦
.
If you can please explain 009

Answer 1

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.