A descent vehicle landing on Mars has a vertical velocity toward the surface of Mars of 6.0 m/s. At the same time, it has a horizontal velocity of 3.5 m/s. At what speed does the vehicle move along it's decent path? At what angle with the vertical is this path?
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To determine the speed of the vehicle along its descent path and the angle of this path with the vertical, we can use vector addition.
First, we need to find the magnitude of the descent velocity. We can use the Pythagorean theorem to calculate the total velocity vector (V) of the vehicle:
V = sqrt(vertical_velocity^2 + horizontal_velocity^2)
Plugging in the values provided:
V = sqrt(6.0^2 + 3.5^2)
V = sqrt(36 + 12.25)
V = sqrt(48.25)
V ≈ 6.95 m/s
So, the speed of the vehicle along its descent path is approximately 6.95 m/s.
Next, we need to find the angle of the descent path with the vertical. We can use trigonometry to calculate this angle.
tan(angle) = vertical_velocity / horizontal_velocity
Plugging in the values provided:
tan(angle) = 6.0 / 3.5
angle ≈ tan^(-1)(6.0 / 3.5)
angle ≈ 61.0 degrees
Therefore, the angle between the descent path and the vertical is approximately 61.0 degrees.