As a prank, your friends have kidnapped you in your sleep, and transported you o

Question

As a prank, your friends have kidnapped you in your sleep, and transported you out onto the ice covering a local pond. When you wake up you are 27.1 m from the nearest shore. The ice is so slippery (i.e. frictionless) that you cannot seem to get yourself moving. You realize that you can use Newton's third law to your advantage, and choose to throw the heaviest thing you have, one boot, in order to get yourself moving. Take your weight to be 575 N.

1) (a) If you throw your 1.14-kg boot with an average force of 458 N, and the throw takes 0.617 s (the time interval over which you apply the force), what is the magnitude of the force that the boot exerts on you? (Assume constant acceleration.)

2) (b) How long does it take you to reach shore, including the short time in which you were throwing the boot?

Explanation / Answer

a) By the third Newton's Law, an object over which is exerted a force F1 reacts and exerts the same force in magnitude but opposite direction

F2=F1 (relation in force magnitudes) and F2=-F1 (relation of force vectors)

therefore, if you throw the boot with a force of F1=458N then the magnitud of the force that the boot exerts on you is F2=F1= 458 N

b) according to your weight

W=m2g ----------> m2=W/g=(575 N)/(9.81 m/s2)=58.6 Kg

then, as F2=m2a2, then

a2=F2/m2 ----------> a2=(458 N)/(58.6 Kg)=7.82 m/s2

for a time of t1=0.617 s you move with an acceleration of a2=7.82 m/s2. so the distance for this time is

x1=a2t12/2=(7.82 m/s2)(0.617 s)2/2= 1,49 m

and the velocity at this time

v=a2t1=(7.82 m/s2)(0.617 s)= 12.7 m/s

after t1 your motion is a constant speed of v= 12.7 m/s and the distance to the shore is x2= (27.1 m - x1)

x2=vt2   ----------> t2 = x2/v = (27.1 m - x1)/v = (27.1 m - 1.49 m)/(12.7 m/s)= 2.02 s

therefore, T= t1 + t2 = 0.617s - 2.02s = 2.64 s

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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