Final answer:
To determine the amount of time it will take for the arrow to hit the ground, we can use the equations of projectile motion to find the horizontal and vertical components of the initial velocity. With the given values of initial speed and angle of launch, we can calculate the time of flight and range of the arrow.
Step-by-step explanation:
To determine the amount of time it will take for the arrow to hit the ground, we can use the equations of projectile motion. The horizontal component of the initial velocity will remain constant throughout the motion. Given that the initial speed is 34.6 m/s and the angle of launch is 24°, we can determine the horizontal component of the initial velocity:
Horizontal component of velocity = initial speed * cos(angle)
Next, we can calculate the time of flight using the equation:
Time of flight = 2 * vertical component of velocity/acceleration due to gravity
Since the arrow is shot at an angle from the horizontal, we need to find the vertical component of the initial velocity:
Vertical component of velocity = initial speed * sin(angle)
Finally, we can find the range of the arrow by multiplying the horizontal component of the initial velocity by the time of flight:
Range = horizontal component of velocity * time of flight