Problem 8 It is apocalyptic future, and zombies are trying to take over the worl

Question

Problem 8 It is apocalyptic future, and zombies are trying to take over the world. In an effort to save the people, our hero aims his bow at a zombie that is slowly approacing them. The zombie is walking towards them at 1.25 m/s He fires the arrow at 20° above the horizon, hits the zombie, and saves the day Varrow-90.0 m/s Vzambie 1.25 m/s a. Given that the bow will fire an arrow at a speed of 90.0 m/s, and assuming that the arrow beging and ends at the same height, how far away is the zombie (distance d) when our hero fires the shot? b. Find the direction and magnitude of the arrow's velocity relative to the zombie just before the arrow hits him.

Explanation / Answer

let us assume that the arrow hits the zombie at time t seconds after being fired.

Now, when the arrow hits the zombie, the y displacement of the arrow is 0mts. The initial velocity in the y direction is 90sin(20)

Using kinematic equation of motion s = u*t -0.5*g*t^2 and substituting the values, we get

0= 90 sin(20) - 0.5*10*t^2

Solving for t we get, t= 6.156 seconds

But during this time t the zombie has moved ahead with a velcity of 1.25m/s as mentioned

The distance covered is 1.25*6.15= 7.695 mts

Hence the arrow hits the zombie at d-7.695 mts from the observer

The arrow's velocity in the x direction is v*cos(20)= 90*0.939= 84.57 m/s

**If you found my explanation useful please do upvote! And in case you have any queries please do leave a
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