An archer stands on a cliff that is 100m high, shooting at a mark on the ground

Question

An archer stands on a cliff that is 100m high, shooting at a mark on the ground
below 430m away from the bottom of the (vertical) cliff. The archer is capable of
shooting an arrow with an initial speed of 35m/s at any angle you choose.
A) If the archer shoots horizontally (at an angle of 0° with respect to the
horizontal), will the arrow reach the mark? Why? If not, will shooting at any angle
above the horizontal help? Why or why not? Be quantitative in your reason.
B) What initial speed of the arrow is needed to be in order for the arrow to reach
the target mark (still with an angle of 0°)?

Explanation / Answer

A) Find the time the arrow hits the ground=t 0.5*g*t^2 = 100m t^2 = 20 s^2 t = 4.47 s. The arrow travels 4.47s*35m/s = 156 m < 430m. Arrow will not reach target. Firing the arrow at 45 degrees would maximize horizontal distance. 0.5*g*t^2 = vtsin45 + 100 t = 7.59 s Arrow travels 7.59s*35cos45 m/s = 188 m < 430m. The arrow will not reach the target not matter what angle it is shot at. All other angles will not go as far as 45 degrees. B) v*4.47s = 430 m v = 430/4.47 m/s = 96 m/s Needs a minimum of 96 m/s initial velocity to hit target if angle is 0.

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