Final answer:
The arrow will go approximately 103 meters.
Step-by-step explanation:
To determine how far the arrow will go, we need to break down its initial velocity into horizontal and vertical components. The horizontal component is given by the formula: Vx = V * cos(theta). Plugging in the values, we get Vx = 46 m/s * cos(38°) ≈ 36 m/s. The time taken for the arrow to reach the highest point can be found using the formula: t = Vy / g, where Vy is the vertical component of the velocity and g is the acceleration due to gravity. Here, Vy = V * sin(theta) = 46 m/s * sin(38°) ≈ 28 m/s. Substituting the values, we get t = 28 m/s / 9.8 m/s² ≈ 2.86 s. Finally, we can find the horizontal distance traveled by multiplying the horizontal component of velocity by the time: d = Vx * t. Substituting the values, we get d ≈ 36 m/s * 2.86 s ≈ 103 m. Therefore, the arrow will go approximately 103 meters.