The problem reads : You are riding your motorcycle one day down a wet street that slopes downward at an angle of 20 ∘ below the horizontal. As you start to ride down the hill, you notice a construction crew has dug a deep hole in the street at the bottom of the hill. A Siberian tiger, escaped from the City Zoo, has taken up residence in the hole. You apply the brakes and lock your wheels at the top of the hill, where you are moving with a speed of 20 m/s. The inclined street in front of you is 40 m long.
A)Will you plunge into the hole and become the tiger’s lunch, or do you skid to a stop before you reach the hole? (The coefficients of friction between your motorcycle tires and the wet pavement are μs=0.90 and μk=0.70.
2. Relevant equations
F_fr = μN
∑F = ma
∑F_net = ma = μN – mg sin70
3. The attempt at a solution
I combined all of the equations above canceling out the mass to get an acceleration of 2.452 m/s^2. I then used a kinematics equation V_x = V_o + at to find that the time to reach 0 m/s speed was 12.23 s. (This number seems large to me). I then used another kinematics equation Dx = v_ot + 1/2 at^2. I found the distance by the man to be something around 183m. This does not seem right to me, but I don’t know where my logic is flawed. Could someone check me on this?