In this 2-dimensional graph, the x-component of each vector is the horizontal distance from the origin, while the y-component of each vector is the vertical distance from the origin. It can be seen that the c vector is 1 vertical unit away from the origin, which means that it has a y-component of 1.
Answer:B
Explanation:
Given
Distance of astronaut From asteroid x is 
Distance of astronaut From asteroid Y is 
Suppose M,M_x,M_y be the masses of Astronaut , asteroid X and Y
If the astronaut is in equilibrium then net gravitational force on it is zero


cancel out the common terms we get




Answer:
U = 1794.005 × 10⁶ J
Explanation:
Data provided;
Capacitance of the original capacitor, C = 1.27 F
Potential difference applied to the original capacitor, V = 59.9 kV
= 59.9 × 10³ V
Now,
The Potential energy (U) for the capacitor is calculated as:
Potential energy of the original capacitor, U =
× C × V²
on substituting the respective values, we get
U =
× 1.27 × ( 59.9 × 10³ )²
or
U = 1794.005 × 10⁶ J
Answer:

Explanation:
For this case we know that the initial velocity is given by:

The final velocity on this case is given by:

And we know that it takes 8 seconds to go from 7m/s to 13m/s. We can use the following kinematic formula in order to find the acceleration during the first interval:

If we solve for the acceleration we got:

So for the other traject we assume that the acceleration is constant and the train travels for 16 s. The initial velocity on this case would be 13m/s from the first interval and we can find the final velocity with the following formula:

And if we replace we got:

<span>As seen by Barbara, Neil is traveling at a velocity of 6.1 m/s at and angle of 76.7 degrees north from due west.
Let's assume that both Barbara and Neil start out at coordinate (0,0) and skate for exactly 1 second. Where do they end up?
Barbara is going due south at 5.9 m/s, so she's at (0,-5.9)
Neil is going due west at 1.4 m/s, so he's at (-1.4,0)
Now to see Neil's relative motion to Barbara, compute a translation that will place Barbara back at (0,0) and apply that same translation to Neil. Adding (0,5.9) to their coordinates will do this.
So the translated coordinates for Neil is now (-1.4, 5.9) and Barbara is at (0,0).
The magnitude of Neil's velocity as seen by Barbara is
sqrt((-1.4)^2 + 5.9^2) = sqrt(1.96 + 34.81) = sqrt(36.77) = 6.1 m/s
The angle of his vector relative to due west will be
atan(5.9/1.4) = atan(4.214285714) = 76.7 degrees
So as seen by Barbara, Neil is traveling at a velocity of 6.1 m/s at and angle of 76.7 degrees north from due west.</span>