A descent vehicle landing on the moon has
a vertical velocity toward the surface of the moon of 34.1 m/s. At the same time, it has a horizontal velocity of 51.1 m/s.
At what speed does the vehicle move along
its descent path?
1.Answer in units of m/s.
2.At what angle with the vertical is its path? Answer in units of ◦.
I already answered the first part but I'm having trouble with the 2nd.
Draw a velocity diagram. You will see that
tanθ = horizontalspeed/verticalspeed
To find the speed at which the vehicle moves along its descent path, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the vertical velocity is one of the sides, and the horizontal velocity is the other side. We can find the magnitude of the resultant velocity (the speed along the descent path) by taking the square root of the sum of the squares of the two side velocities.
Let's calculate it:
Speed along descent path = square root of (vertical velocity^2 + horizontal velocity^2)
= square root of (34.1^2 + 51.1^2)
= square root of (1162.81 + 2616.21)
= square root of 3779.02
≈ 61.49 m/s
Therefore, the speed at which the vehicle moves along its descent path is approximately 61.49 m/s.
Now, let's find the angle of the descent path with the vertical. The angle can be determined using trigonometry. The tangent of the angle is equal to the ratio of the vertical velocity to the horizontal velocity.
Let's calculate it:
Angle = arctan(vertical velocity / horizontal velocity)
= arctan(34.1 / 51.1)
≈ arctan(0.667)
Using a scientific calculator, we find that the angle is approximately 33.12 degrees.
Therefore, the angle with the vertical is approximately 33.12 degrees.