Question
Juana and Diego Gonzales, ages six and four respectively, own a strong and stubborn puppy named Corporal. It is so hard to take Corporal for a walk that they devise a scheme to use two leashes. If Juana pulls with a force of 23 lbs at an angle of 18° and Diego pulls with a force of 27 lbs at an angle of -15°, how hard is Corporal pulling if the puppy holds the children at a standstill?
Im trying to figure out how to set this up?
Im trying to figure out how to set this up?
Answers
Reiny
let AP be the vector of magnitude 23 lbs and direction 18°
and BP be the vector of magnitude 27 lbs and direction -15°
Complete the parallogram APBQ , with
AP=2
BP=27
angle P = 33°
then angle B = 180-33 = 147°
So PQ is the force pulling by the puppy to hold the kids
In triangle BPQ
BP=27
BQ=23
angle B=147
PQ^2 = 23^2 + 27^2 - 2(23)(27)cos147
PQ^2 = 2299.628...
PQ = √...
= 47.95 lbs
and BP be the vector of magnitude 27 lbs and direction -15°
Complete the parallogram APBQ , with
AP=2
BP=27
angle P = 33°
then angle B = 180-33 = 147°
So PQ is the force pulling by the puppy to hold the kids
In triangle BPQ
BP=27
BQ=23
angle B=147
PQ^2 = 23^2 + 27^2 - 2(23)(27)cos147
PQ^2 = 2299.628...
PQ = √...
= 47.95 lbs