Final answer:
To calculate the time it took for the arrow to reach the target, we use the formula for vertical displacement under gravity. The arrow's descent of 52 cm provides the vertical displacement needed to solve for time, yielding approximately 0.325 seconds.
Step-by-step explanation:
The student's question deals with the physics of projectile motion, specifically calculating the time it takes for an arrow, shot horizontally, to reach a target. Since the arrow was aimed directly at the center but hit 52 cm lower, we need to calculate the time of flight based solely on the vertical displacement due to gravity, as horizontal motion is independent of vertical motion in projectile problems.
Using the formula for vertical displacement under constant acceleration, which in this case is due to gravity (g = 9.81 m/s2), we have:
y = 0.52 m (since the arrow fell 52 cm)
Initial velocity (Vi) = 0 m/s (as the arrow is shot horizontally, it has no initial vertical velocity)
Acceleration due to gravity (g) = 9.81 m/s2
The formula for vertical displacement is y = Vi * t + (1/2) * g * t2. Plugging in the values we get:
0.52 m = 0 m/s * t + (1/2) * 9.81 m/s2 * t2
After simplification, we are left with a quadratic equation in terms of t:
0 = t2 + (0.52 m / (1/2 * 9.81 m/s2))
0 = t2 + (0.52 m / 4.905 m/s2)
0 = t2 + 0.1059 s2
The positive root of this equation will give us the time it took for the arrow to hit the target. Applying the square root to 0.1059 s2, we find:
t ≈ 0.325 s
Therefore, it took approximately 0.325 seconds for the arrow to reach the target.