Will bob will be able to stop his car before hitting the tree branch

Question

Bob is driving his 2400 kg car on a wet road at 50 mph when he sees a tree branch in the middle of the road 60 meters ahead of him and immediately slams on the breaks. If the coefficient of friction between the car’s tires and the road is 0.41, will Bob be able to stop his car before hitting the tree branch

Answer 1

Gabby,

 

You already posted a few questions very similar to this one, which were already answered.  I suggest you examine those solutions and apply the same method to this problem.  But I will set this up for you anyway, and you work the math.  

 

x = required stopping distance, based on initial speed and braking force, = ?

 

v_i = intial speed (given)

 

v_f = final speed = 0 (full stop)

 

μ = coefficient of kinetic friction (given)

 

Use the kinematic relation

 

v_f² - v_i² = 2ax

 

a = -f/m = -μmg/m = -μg  [negative, since it opposes the direction of motion]

 

0² - v_i² = 2(-μg)x

 

x = v_i² / (2μg)

 

Compute x (being careful with the units), compare x to the available stopping distance of 60 m, and you will have your answer.  You should be able to finish from here.  Try working these problems, and you will learn from the process.