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

range=vox*tt=range/vox=430/3512.3 s but (2*100/9.8)4.52 s

A) vo=vox=35 m/s*4.52 s158 m from cliff, arrow will not reach 430 m

away from cliff, shooting at any angle will not reach 430 m on the ground

if (430*9.8/sin(2*45o))64.92 m/s at 45o is necessary to reach 430 m

B) 100 m=0+1/2*9.8*t2=4.5176 s==>430 m/4.5176 s95.18 m/s

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