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

Question

An archer stands on a cliff that is 100m high, shooting at a markon the ground below 430m away from the bottom of the (vertical)cliff. The archer is capable of shooting an arrow with an initialspeed of 35 m/s at any angle you choose.

A) If the archer shoots horizontally ( at an angle of zero degreeswith 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?

B) What initial speed of the arrow is needed to be in order for thearrow to reach the target mark ( still with an angle of zerodegrees)?

Explanation / Answer

The velocity in the x direction is constant and it equals the initial velocity v0 = 35 m/s. The y direction velocity equals gt. Hence, the path in the x direction equals v0*t = 35*t (1), and in the y direction 0.5*g*t^2. Now if the arrow falls to the ground, the path that it has to cross in the y direction equals 100 m, so 0.5*g*t^2=100. Solving this equation gives us the time t of the flight of the arrow. Putting that time into equation (1) gives us the x displacement of the arrow, so we can tell if it has his the target or not.

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