Answer:
= 0.0009866 N
Step-by-step explanation:
For resolving this problem we can use the impulse-momentum theorem; this theorem establishes that the change in momentum of an object equals the impulse applied to it
The impulse is defined how:
I = Δt
: Average force
Δt = Time interval
Then:
Δt
(0.048)(14) - (0.048)(-23) = (1800)
0.672 + 1.104 = 1800
1.776 = 1800
=
= 0.0009866 N
Explanation:
A rhombus is a parallelogram in which the diagonals are mutual perpendicular bisectors. The coordinates of the vertices can be used to show ...
When both these conditions are met, the quadrilateral is a rhombus.
__
<h3>Mutual Bisectors</h3>The diagonals will have the same midpoint (bisect each other) if the sum of the coordinates at the ends of one diagonal is the same as the sum of the end point coordinates of the other diagonal:
A +C = B +D
(3, 6) +(9, 6) = (6, 8) +(6, 4)
(3+9, 6 +6) = (6 +6, 8 +4)
(12, 12) = (12, 12) . . . . . . midpoints are the same; ABCD is a parallelogram
__
<h3>Perpendicular</h3>The diagonals will be perpendicular if the sum of the products of the coordinate differences of their end points is zero.
AC⋅BD = (C -A)⋅(D -B) = (9 -3, 6 -6)⋅(6 -6, 4 -8)
= (6, 0)⋅(0, -4) . . . . . end point differences; we want their dot-product
= (6)(0) +(0)(-4) = 0 +0 = 0 . . . . diagonals are perpendicular
_____
<em>Additional comment</em>
The midpoints are computed as (A+C)/2 and (B+D)/2. We have multiplied each of them by 2 to simplify the arithmetic. Our resulting sums of (12, 12) must be divided by 2 to get the actual midpoint of the rhombus: (6, 6).
The notion of "dot product" is a vector notion. Two vectors are perpendicular when their dot product is zero. The dot product is the scalar sum of the products of corresponding coordinates.
