Question

1. solve for the unknowns

find the two forces.
kelsha:
343n
allie:
421.4n
define keisha’s distance in terms of the length of the seesaw and
allie’s distance.
when there is no rotation, the sum of the torques is zero.
solve for ( r_a ) and ( r_k ).

Explanation:

Step1: Set up torque equilibrium

Let $L$ = length of seesaw, $r_K$ = Keisha's distance, $r_A$ = Allie's distance. Torque balance: $F_K r_K = F_A r_A$, so $343r_K = 421.4r_A$.

Step2: Relate distances to seesaw length

$r_K + r_A = L$, so $r_A = L - r_K$.

Step3: Substitute $r_A$ into torque equation

$343r_K = 421.4(L - r_K)$
$343r_K + 421.4r_K = 421.4L$
$764.4r_K = 421.4L$
$r_K = \frac{421.4}{764.4}L \approx 0.551L$

Step4: Solve for $r_A$

$r_A = L - 0.551L = 0.449L$

Answer:

Keisha's distance: $r_K \approx 0.551L$ (where $L$ is the seesaw length)
Allie's distance: $r_A \approx 0.449L$ (where $L$ is the seesaw length)