Answer
a) $\Delta t=2\times 10^{-7}s$
b) $d=53.46m$
c) $d=7.72m$
Work Step by Step
(a) We know that
$\Delta t=\frac{\Delta t}{\sqrt{1-\frac{v^2}{c^2}}}$
We plug in the known values to obtain:
$\Delta t=\frac{2.6\times 10^{-8}s}{\sqrt{1-\frac{(0.99c)^2}{c^2}}}$
$\Delta t=2\times 10^{-7}s$
(b) As $d=v\Delta t$
We plug in the known values to obtain:
$d=(0.99c)(1.8\times 10^{-7}s)$
$d=(0.99)(3\times 10^8m/s)(1.8\times 10^{-7}s)$
$d=53.46m$
(c) We know that
$d=v\Delta t_{\circ}$
We plug in the known values to obtain:
$d=(0.99c)(2.6\times 10^{-8}s)$
$d=(0.99)(3\times 10^8m/s)(2.6\times 10^{-8}s)$
$d=7.72m$
