A Woman Running Towards a Bus Which Pulls away

[Phonetic]

Homework Statement

A woman is running at a constant velocity of 5.0m/s in an attempt to catch a bus. When she is 11m from the bus, it pulls away with a constant acceleration of +1.0m/s². From this point, how much time does it take her to reach the bus if she keeps running with the same velocity?



2. The attempt at a solution
Finding the time
d = d_i + v_it+1/2at²
0 = 11 + 0t + 1/2(1)t²
0 = 11 + .5t²
t = sqrt of 11.5
t = 3.39

Distance traveled by woman
d = v*t
d = 5*3.39
d = 16.95m

Distance traveled by bus
v_f = v_i + at
= 0+1*3.39
v_f = 3.39

d = 1/2 (v_i + v_f)t
d = 1/2 (3.39) 3.39
d = 1/2 * 11.5
d = 5.75
The bus traveled 5.75m, add in the initial distance of 11m
16.75m

That's the closest I can get to the answer. Any guidance on where I want wrong? Thanks!

 

[stauber28]

Set your initial position to Zero for woman, and initial position to 11 for the bus. Set these two equations equal to solve.

Woman d1=0+5t
Bus d2=11+.5t²

When both positions are equal she will reach the bus
d1=d2

5t = 11+.5t²
10t-t² = 22
t=5±√3

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