# Chapter 2 - Motion Along a Straight Line - Problems: 52a

$t\approx.452s$

#### Work Step by Step

The total time for the bolt to fall can be calculated from the equation $x=\frac{1}{2}gt^{2}$. Solving for $t$, we get $t=\sqrt {\frac{2x}{g}}$. The time it takes for the bolt to hit the ground is $t_{1}=\sqrt {\frac{2(90m)}{(9.8m/s^{2})}}\approx4.29s$ The time it takes for the bolt to pass through $80$% of its fall is $t_{2}=\sqrt {\frac{2(90m)(.8)}{(9.8m/s^{2})}}\approx3.83s$ The difference between these two times is the amount of time that passes during the last $20$% of the fall: $t=t_{1}-t_{2}=4.29s-3.83s=.452s$

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