Certainly! To find the magnitude of the resultant momentum after the collision, we need to combine the given [tex]\( y \)[/tex]-momentum and [tex]\( x \)[/tex]-momentum using the Pythagorean theorem.
Given:
- [tex]\( y \)[/tex]-momentum = 98 kg·m/s
- [tex]\( x \)[/tex]-momentum = 100 kg·m/s
The resultant momentum [tex]\( p_{\text{resultant}} \)[/tex] can be calculated using the formula for the magnitude of a vector:
[tex]\[
p_{\text{resultant}} = \sqrt{(p_x^2 + p_y^2)}
\][/tex]
Let's plug in the values:
[tex]\[
p_{\text{resultant}} = \sqrt{(100^2 + 98^2)}
\][/tex]
First, compute the squares:
[tex]\[
100^2 = 10000
\][/tex]
[tex]\[
98^2 = 9604
\][/tex]
Next, add these values:
[tex]\[
10000 + 9604 = 19604
\][/tex]
Finally, take the square root of the sum:
[tex]\[
\sqrt{19604} \approx 140.0142849854971
\][/tex]
Thus, the magnitude of the resultant momentum is approximately [tex]\( 140.014 \)[/tex] kilogram meters/second.
Looking at the given options:
A. [tex]\( 1.0 \times 10^2 \)[/tex] kilogram meters/second
B. [tex]\( 1.3 \times 10^2 \)[/tex] kilogram meters/second
C. [tex]\( 1.3 \times 10^2 \)[/tex].ilogram meters/second
D. [tex]\( 1.4 \times 10^2 \)[/tex] kilogram meters/second
E. [tex]\( 1.8 \times 10^2 \)[/tex] kilogram meters/second
The correct choice is:
D. [tex]\( 1.4 \times 10^2 \)[/tex] kilogram meters/second
