Question

Two reindeer-in-training pull on a sleigh. Connie pulls with a force of 200 N at an angle of 20 degrees above the (positive) -axis, while Randolph pulls with a force of 800 N at an angle of 50 degrees ° below the positive) -axis. What is their resultant magnitude of the force on the sleigh?

Answer 1

Answer:

$F_r \approx 978.3N$

$\theta =44 \textdegree$

Explanation:

From the question we are told that

Connie pulls with a force of $F_c=200 N$

At an angle $\theta _c=20 \textdegree$

Randolph pulls with a force of $F_R=800 N$

At an angle $\theta _R=50 \textdegree$

Generally the horizontal axis  can mathematically be represented as

$f_x=f_ccos\theta _c+F_Rcos\theta _R$

$f_x=200*cos20+800*cos50$

$f_x=702.2N$

Generally the vertical axis  can mathematically be represented as

$f_y=f_csin\theta _c+F_Rsin\theta _R$

$f_y=200*sin20+800*sin50$

$f_y=681.24N$

Generally the resultant force $F_r$ is mathematically  given by

$F_r=\sqrt{f_x^2+f_y^2}$

$F_r=\sqrt{702.1686119^2+681.2395832^2}$

$F_r=978.3230731N$

$F_r \approx 978.3N$

Generally the Direction $\theta$ of force is mathematically given by

$\theta =tan^-^1(\frac{f_c}{f_y})$

$\theta =tan^-^1(\frac{681.23}{702.16})$

$\theta =44 \textdegree$