Final answer:
The initial velocity of the arrow is approximately 163.27 m/s.
Step-by-step explanation:
To solve this problem, we can use the equations of projectile motion. Since the crossbow is aimed horizontally, the initial vertical velocity of the arrow is zero. The arrow will only be affected by the force of gravity.
We can use the equation:
y = (1/2) * g * t^2
Where y is the vertical displacement, g is the acceleration due to gravity (9.8 m/s^2), and t is the time of flight.
In this case, the vertical displacement is 30 cm below the target, which is -0.3 m. Plugging in the values, we can solve for t:
-0.3 = (1/2) * 9.8 * t^2
t^2 = (-0.3 * 2) / 9.8
t^2 = -0.06
t = 0.245 s
Now, we can find the horizontal velocity by using the equation:
x = v * t
Where x is the horizontal displacement, v is the initial velocity, and t is the time of flight.
In this case, the horizontal displacement is 40 m. Plugging in the values, we can solve for v:
40 = v * 0.245
v = 40 / 0.245
v = 163.27 m/s
The initial velocity of the arrow is approximately 163.27 m/s.