If we have the angle and magnitude of a vector A we can find its Cartesian components using the following formula
![A_x = |A|cos(\alpha)\\\\A_y = |A|sin(\alpha)](https://tex.z-dn.net/?f=A_x%20%3D%20%7CA%7Ccos%28%5Calpha%29%5C%5C%5C%5CA_y%20%3D%20%7CA%7Csin%28%5Calpha%29)
Where | A | is the magnitude of the vector and
is the angle that it forms with the x axis in the opposite direction to the hands of the clock.
In this problem we know the value of Ax and Ay and we need the angle
.
Vector A is in the 4th quadrant
So:
![A_x = 6\\\\A_y = -6.5](https://tex.z-dn.net/?f=A_x%20%3D%206%5C%5C%5C%5CA_y%20%3D%20-6.5)
So:
![|A| = \sqrt{6^2 + (-6.5)^2}\\\\|A| = 8.846](https://tex.z-dn.net/?f=%7CA%7C%20%3D%20%5Csqrt%7B6%5E2%20%2B%20%28-6.5%29%5E2%7D%5C%5C%5C%5C%7CA%7C%20%3D%208.846)
So:
![Ay = -6.5 = 8.846cos(\alpha)\\\\sin(\alpha) = \frac{-6.5}{8.846}\\\\sin(\alpha) = -0.7348\\\\\alpha = sin^{- 1}(- 0.7348)](https://tex.z-dn.net/?f=Ay%20%3D%20-6.5%20%3D%208.846cos%28%5Calpha%29%5C%5C%5C%5Csin%28%5Calpha%29%20%3D%20%5Cfrac%7B-6.5%7D%7B8.846%7D%5C%5C%5C%5Csin%28%5Calpha%29%20%3D%20-0.7348%5C%5C%5C%5C%5Calpha%20%3D%20sin%5E%7B-%201%7D%28-%200.7348%29)
= -47.28 ° +360° = 313 °
= 313 °
Option 4.
a)
Y₀ = initial position of the stone at the time of launch = 0 m
Y = final position of stone = 20.0 meters
a = acceleration = - 9.8 m/s²
v₀ = initial speed of stone at the time of launch = 30.0 m/s
v = final speed = ?
Using the equation
v² = v₀² + 2 a (Y - Y₀)
inserting the values
v² = 30² + 2 (- 9.8) (20 - 0)
v = 22.5 m/s
b)
Y₀ = initial position of the stone at the time of launch = 0 m
Y = maximum height gained
a = acceleration = - 9.8 m/s²
v₀ = initial speed of stone at the time of launch = 30.0 m/s
v = final speed = 0 m/s
Using the equation
v² = v₀² + 2 a (Y - Y₀)
inserting the values
0² = 30² + 2 (- 9.8) (Y - 0)
Y = 46 m
The weight is not coming from the center of the mass because the force that act on it is not is equal is side.(2) section B donot have weight because the ruler bend down and section be raise up so no weight.
Answer:
not clear pic...but it's definitely not A)