Answer to Question #172451 in Physics for Dashaun

Question

An archer on the set of Game of Thrones is set to shoot an arrow during a scene where a person is riding towards the castle. The archer is on the wall of a castle that is 20 meters above the ground and is only allowed to shot the arrow straight ahead and not at an angle. The rider on the horse is 2.5 meters off the ground.

a. Determine the amount of time the arrow is in the air after being shot before it hits the rider. Show your work.

b. Determine the velocity that the arrow has to be traveling at when it leaves the bow if the rider is hit 200 meters away. Show your work.

c. Create a Horizontal Velocity vs Time Graph demonstrating the motion of the arrow after the launch.

d. Create a Vertical Velocity vs Time Graph demonstrating the motion of the arrow after the launch.

Answer 1

a)

$$y=\dfrac{1}{2}gt^2,$$ $$t=\sqrt{\dfrac{2y}{g}}=\sqrt{\dfrac{2\cdot(20\ m-2.5\ m)}{9.8\ \dfrac{m}{s^2}}}=1.89\ s.$$

b)

$$x=v_0t,$$ $$v_0=\dfrac{x}{t}=\dfrac{200\ m}{1.89\ s}=106\ \dfrac{m}{s}.$$

c) Let's plot the Horizontal Velocity vs Time Graph:

d) Let's plot the Vertical Velocity vs Time Graph: