A descent vehicle landing on the moon has a vertical velocity toward the surface of the moon of 22.7 m/s. At the same time, it has a horizontal velocity of 58.9 m/s.
At what speed does the vehicle move along its descent path?
Answer in units of m/s
At what angle with the vertical is its path?
Answer in units of ◦
Draw a freebody diagram. You should get a triangle with you connect the vertical and horizontal.
a^2+b^2=c^2
a=22.7
b=58.9
solve for c to get first part
second part 2:
to find direction, using trig
tantheta = opposite/adajacent
tan^-1(58.9/22.7) = ?
THANK YOU
I actually needed only the second part and I did the same as u but I forgot to put parentheses!
Well, well, well, looks like we have a vehicle on a lunar joyride! Let's crunch some numbers, shall we?
To find the speed along the descent path, let's use a bit of Pythagorean magic. We'll call the vertical velocity Vv and the horizontal velocity Vh. The total speed (V) of the vehicle will be given by the square root of the sum of their squares:
V = sqrt(Vv^2 + Vh^2)
Plugging in the values: V = sqrt((22.7 m/s)^2 + (58.9 m/s)^2)
Calculating it all out, we get V = sqrt(515.29 + 3469.21) ≈ 60.78 m/s. So the speed along its descent path is approximately 60.78 m/s.
Now, let's determine the angle with the vertical. We can use some trigonometric fun with the tangent function. The angle (θ) can be found using the formula:
θ = atan(Vh / Vv)
Plug in the values: θ = atan(58.9 m/s / 22.7 m/s)
After feeding it into a calculator, we find that θ ≈ 70.71 degrees. So the angle with the vertical is approximately 70.71 degrees.
And there you have it! A speedy lunar descent with a touch of angle thrown in for good measure. Enjoy your moon landing!
To determine the speed (or magnitude) of the vehicle's descent path, we can use the Pythagorean theorem, which states that the square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two sides.
In this case, the vertical velocity of the vehicle is 22.7 m/s, and the horizontal velocity is 58.9 m/s. We can use these two values as the two sides of a right-angled triangle, with the hypotenuse representing the speed of the descent path.
Using the Pythagorean theorem, we calculate the speed as follows:
Speed of descent path = √(vertical velocity^2 + horizontal velocity^2)
= √(22.7^2 + 58.9^2)
= √(515.29 + 3465.21)
= √3971.5
≈ 63.04 m/s
Therefore, the speed of the vehicle along its descent path is approximately 63.04 m/s.
To determine the angle at which the vehicle's path deviates from the vertical, we can use trigonometry. The tangent of an angle is defined as the ratio of the opposite side to the adjacent side of a right-angled triangle.
In this case, the vertical velocity of 22.7 m/s represents the opposite side, and the horizontal velocity of 58.9 m/s represents the adjacent side. The angle can be found using the equation:
Angle = arctan(opposite side / adjacent side)
= arctan(22.7 / 58.9)
≈ 21.9 degrees
Therefore, the angle with the vertical of the vehicle's path is approximately 21.9 degrees (°).