Understanding the Physics

* Constant Acceleration: The arrow is subject to the constant acceleration due to gravity, which is approximately -9.8 m/s² (negative because it acts downwards).

* Kinematic Equations: We can use the following kinematic equation to relate displacement, initial velocity, acceleration, and time:

* Δy = v₀t + (1/2)at²

Variables

* Δy = 33.0 m (vertical displacement)

* t = 2.0 s (time)

* a = -9.8 m/s² (acceleration due to gravity)

* v₀ = ? (initial velocity, what we want to find)

Solving for Initial Velocity (v₀)

1. Plug the values into the equation:

33.0 m = v₀(2.0 s) + (1/2)(-9.8 m/s²)(2.0 s)²

2. Simplify and solve for v₀:

33.0 m = 2.0v₀ - 19.6 m

52.6 m = 2.0v₀

v₀ = 26.3 m/s

Answer: The initial velocity of the arrow is 26.3 m/s.