Question

An archer shoots an arrow horizontally at a target 15 m away. The arrow is aimed directly at the center of the target, but it hits 52 cm lower. How long did it take for the arrow to reach the target?

a) 1.2 seconds
b) 1.5 seconds
c) 1.8 seconds
d) 2.0 seconds

Answer 1

To find the time it took for the arrow to reach the target, we can use the equations of motion for horizontal and vertical motion. The time is approximately 0.326 seconds, which does not match any of the given options.

Step-by-step explanation:

To solve this problem, we can use the equations of motion for horizontal and vertical motion.

First, let's solve for the time it takes for the arrow to reach the target.

Since the arrow is shot horizontally, its initial vertical velocity () is 0 m/s.

The vertical displacement () of the arrow is 52 cm, which is equivalent to 0.52 m.

Using the equation = + 0.5^2, where is the initial vertical velocity, is the time, and is the vertical acceleration (which is -9.8 m/s^2 for objects in free fall), we can solve for :

0.52 = 0 × + 0.5 × (-9.8) × ^2

Simplifying the equation, we get:

4.9^2 = 0.52

^2 = 0.52/4.9

^2 = 0.106

≈ √0.106

≈ 0.326 s

Therefore, it took approximately 0.326 seconds for the arrow to reach the target. None of the given options match the calculated time, so none of the provided options are correct.