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A lunar astronaut hit a golf ball off of a golf 'tee'. The impact was slightly off-center and the errant shot barely cleared a hill and when found, the ball had landed in the very bottom of a crater. The information that you have available is:

  • On the Moon, the mass $m$, of the golf ball was $46\text{ g}$.
  • The speed of the golf ball immediately after being struck by the golf club was $39\text{ m/s}$, but the initial angle above the horizontal was not recorded.
  • The height of the hill was $45\text{ m}$ above the tee.
  • The acceleration of gravity on the moon ${g}_{m}$ is $1.6\ \mathrm{m/s^2}$.
  • The bottom of the crater was $33\text{ m}$ below the tee.

From the information given, what was the speed of the golf ball on impact with the bottom of the crater?

A

$37 \text{ m/s}$

B

$4\bar{0 } \text{ m/s}$

C

$42 \text{ m/s}$

D

$46 \text{ m/s}$

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