Answer:
The magnitude of the resultant decreases from A+B to A-B
Explanation:
The magnitude of the resultant of two vectors is given by

where
A is the magnitude of the first vector
B is the magnitude of the second vector
is the angle between the directions of the two vectors
In the formula, A and B are constant, so the behaviour depends only on the function
. The value of
are:
- 1 (maximum) when the angle is 0, so the magnitude of the resultant in this case is

- then it decreases, until it becomes 0 when the angle is 90 degrees, where the magnitude of the resultant is

- then it becomes negative, and continues to decrease, until it reaches a value of -1 when the angle is 180 degrees, and the magnitude of the resultant is

The bullet travels a horizontal distance of 276.5 m
The bullet is shot forward with a horizontal velocity
. It takes a time <em>t</em> to fall a vertical distance <em>y</em> and at the same time travels a horizontal distance <em>x. </em>
The bullet's horizontal velocity remains constant since no force acts on the bullet in the horizontal direction.
The initial velocity of the bullet has no component in the vertical direction. As it falls through the vertical distance, it is accelerated due to the force of gravity.
Calculate the time taken for the bullet to fall through a vertical distance <em>y </em>using the equation,

Substitute 0 m/s for
, 9.81 m/s²for <em>g</em> and 1.5 m for <em>y</em>.

The horizontal distance traveled by the bullet is given by,

Substitute 500 m/s for
and 0.5530s for t.

The bullet travels a distance of 276.5 m.