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 53.5 m/s.
At what speed does the vehicle move along
its descent path?
Answer in units of m/s.
clearly, the speed is
√(34.1^2 + 53.5^2)
To find the speed at which the vehicle moves along its descent path, we can use the concept of vector addition. The descent path of the vehicle is a combination of its vertical velocity (toward the surface of the moon) and its horizontal velocity.
The magnitude of the resulting velocity can be found using the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the vertical velocity (34.1 m/s) is one side of the triangle, and the horizontal velocity (53.5 m/s) is the other side. Let's call the resultant velocity (the hypotenuse) as v.
Using the Pythagorean theorem, we have:
v^2 = (vertical velocity)^2 + (horizontal velocity)^2
v^2 = (34.1 m/s)^2 + (53.5 m/s)^2
v^2 = 1162.81 m^2/s^2 + 2862.25 m^2/s^2
v^2 = 4025.06 m^2/s^2
Taking the square root of both sides to find the magnitude of the velocity:
v = √(4025.06 m^2/s^2)
v ≈ 63.44 m/s
Therefore, the speed at which the vehicle moves along its descent path is approximately 63.44 m/s.