Final answer:
To calculate the initial velocity of the arrow, use the vertical displacement to find the time it was in the air and then divide the horizontal distance by this time.
Step-by-step explanation:
Initial Velocity of the Arrow
To find the initial velocity of the arrow, we can use the kinematic equations for projectile motion. Since the arrow hits 30 cm (0.3 m) below the aim point, we know that this is the distance it fell due to gravity alone. We can start by calculating the time it took for the arrow to fall that 0.3 meters using the equation for vertical displacement s = 1/2gt^2, where g is the acceleration due to gravity (9.8 m/s^2) and t is the time.
After we find the time, we can use it to calculate the initial velocity using the horizontal displacement, which is distance / time. The initial horizontal velocity (v) can be found using the formula v = d/t, where d is the horizontal displacement (40 m).