A man steps out of his vehicle onto an icy, inclined, parking lot. As he steps a

Question

A man steps out of his vehicle onto an icy, inclined, parking lot. As he steps away from his car, his feet slip on the icy surface and he begins to slide. Assuming he started to slide from rest, that icy surfaces are frictionless, and the pavement makes a 15 degree angle from the horizontal, answer the following:

(a) What is the acceleration of the man as he slides down the inclined pavement? Be sure to draw your coordinate system and indicate the positive directions.

(b) How much time does it take the man to slide 10m?

(c) What is his velocity after having traveled this 10m?

(d) What would his acceleration need to be to traverse this 10m in twice the time?

(e) What would be the grade (angle) which would give rise to this acceleration?

(f) 10m from where the man began his slide down the 15 degree slope, the parking lot turns upward at an angle 5 degrees from the horizontal. How much time does it take the man to come to a stop as he slides up this icy hill?

Explanation / Answer

a) a = g*sin(15)

= 9.8*sin(15)

= 2.54 m/s^2

b) d = 0.5*a*t^2

t = sqrt(2*d/a)

= sqrt(2*10/2.54)

= 2.8 s

c) v = u +a*t

= 0 + 2.54*2.8

= 7.13 m/s

d) a' = 4*a

= 4*2.54

= 10.16 m/s^2

e) Approximatey 90 degrees

f) a = -g*sin(5)

= -9.8*sin(5)
= -0.854 m/s^2

Appy, t = v/a

= 7.13/0.854

= 8.35 s

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