J.H. went muddin J.H. went muddin J.H. went muddin\' in his jeep and got it stuc

Question

                

                    J.H. went muddin

                

                    J.H. went muddin

J.H. went muddin' in his jeep and got it stuck. He reckons a force of 500 lb applied in the direction, r2, will be enough to get the jeep out of the mud. The jeep's bumper winch is attached to a nearby tree in the direction, r1, and has a maximum rated pulling force of 1000 lb. Find unit vectors in the directions r1 and r2 using Cartesian notation. Determine if J.H. will be able to pull himself out of the mud.

Explanation / Answer

Find unit vectors for r1 and r2, multiply by 1000 lbs and -500 lbs, respectively, and then add resultant vectors to find net force in lbs. If the force is positive, the Jeep moves. If not, then it doesn't.
(it's -500 lbs because that's how much the Jeep "weighs" in the direction of r2 according to J.H., so that's how much force needs to be overcome)

so F_net= 1000 lbs*r1_unit + -500 lbs*r2_unit

unit vector for r1 is r1/|r1|
for r2 is r2/|r2|

r1= <50, 800, 250>
|r1|= sqrt(50^2+800^2+250^2)

r2= <-4, 8, -2>
|r2|= sqrt(4^2+8^2+2^2)

hence net force=(100/838)*<50, 800, 250>+(500/9.1651)*<-4, 8, -2>=(-212.253, 531.904, -79.2766)

magnitude of force=578.15

Related Questions

Navigate

• Browse (All)
• Browse J
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.