To find the velocity of the propeller:

find the cricumference of the propeller blade:

\(\displaystyle\pi{r}^{{{2}}}=\pi{\left({12}^{{{2}}}\right)}={144}\pi\)

if it travels this distance in 1.2 seconds:

\(\displaystyle{v}={144}\frac{\pi}{{1.2}}={120}\pi\frac{{m}}{{s}}\)

The total height is 32 m, so use equation of motion todetermine the time of flight:

d = 32 m

\(\displaystyle{a}\frac{=}{{9.8}}\frac{{m}}{{s}^{{{2}}}}\)

t = ?

\(\displaystyle{V}_{{{i}}}={0}\)

\(\displaystyle{d}={V}{t}+\frac{{1}}{{2}}{a}{t}^{{{2}}}={2.55}\) seconds

now put this into \(\displaystyle{V}_{{{o}}}=\frac{{x}}{{t}}\) and solve for x:

\(\displaystyle\frac{{V}_{{{o}}}}{{t}}={x}={120}\frac{\pi}{{2.55}}={147.8}{m}\)

so this would correspond to e).

find the cricumference of the propeller blade:

\(\displaystyle\pi{r}^{{{2}}}=\pi{\left({12}^{{{2}}}\right)}={144}\pi\)

if it travels this distance in 1.2 seconds:

\(\displaystyle{v}={144}\frac{\pi}{{1.2}}={120}\pi\frac{{m}}{{s}}\)

The total height is 32 m, so use equation of motion todetermine the time of flight:

d = 32 m

\(\displaystyle{a}\frac{=}{{9.8}}\frac{{m}}{{s}^{{{2}}}}\)

t = ?

\(\displaystyle{V}_{{{i}}}={0}\)

\(\displaystyle{d}={V}{t}+\frac{{1}}{{2}}{a}{t}^{{{2}}}={2.55}\) seconds

now put this into \(\displaystyle{V}_{{{o}}}=\frac{{x}}{{t}}\) and solve for x:

\(\displaystyle\frac{{V}_{{{o}}}}{{t}}={x}={120}\frac{\pi}{{2.55}}={147.8}{m}\)

so this would correspond to e).