Answer:
Correct answer: A) D = 23.05 m B) V = 46.37 m/s , α = 6.19°
Step-by-step explanation:
The fired arrow performs a complex movement called a horizontal shot.
Horizontal shot is the result of the combination of two independent perpendicular movements, horizontal and vertical.
In the horizontal direction the arrow moves at a constant initial velocity
V₀ₓ and in the vertical direction performs a free fall without the initial velocity.
The free fall height is given by the formula
h = g · t²/2 , we take that the gravitational acceleration is g = 10 m/s²
From this formula we will calculate the time of fall, which is also the total time of movement of the arrow in the horizontal direction
t = √(2 h)/g = √(2 · 1.25)/10 = √0.25 = 0.5 seconds
The total distance the arrow reached
D = V₀ₓ · t = 46.1 · 0.5 = 23.05 m
The vertical component of the final velocity is
Vy = g · t = 10 · 0.5 = 5 m/s
We will calculate the total ultimate velocity using Pythagoras' theorem
V = √V₀ₓ² + Vy² = √46.1² + 5² = √2,125.21 + 25 = √2,150.21 = 46.37 m/s
The angle that the arrow will have with respect to the horizon or direction will be found using a tanα
tanα = Vy / V₀ₓ = 5 / 46.1 = 0.1084 => α = tan⁻¹ 0.1084 = 6.19°
α = 6.19°
God is with you!!!