The paintball, shot horizontally at 50 m/s, takes 0.3 seconds to hit a tree 15 meters away. Striking 0.441 meters below the knothole, the vertical distance reflects downward impact.
To solve this problem, we can use the equations of motion. The horizontal motion and vertical motion are independent of each other.
Let's first find the time it takes for the paintball to reach the tree horizontally. We can use the formula:
Horizontal distance = horizontal velocity * time
The horizontal velocity (Vx) is given by the initial speed (50 m/s), and the time of flight (t) can be found from the horizontal distance traveled (15 m).
15 m = 50 m/s * t
t = 15 m / 50 m/s
t = 0.3 s
Now that we know the time of flight, we can find the vertical position of the paintball at that time using the vertical motion equation:
Vertical distance = initial vertical velocity * time + 0.5 * acceleration * time^2
The initial vertical velocity (Vy0) is 0 m/s because the paintball starts from the same height as it lands. The acceleration (g) is the acceleration due to gravity (9.8 m/s^2). The time of flight (t) is 0.3 s.
Vertical distance = 0 * 0.3 + 0.5 * (-9.8) * (0.3)^2
Vertical distance = -0.441 m
The negative sign indicates that the vertical distance is downward. Therefore, the paintball strikes the tree 0.441 m below the knothole.
So, the final answer is that the paintball strikes the tree 0.441 m below the knothole.
Complete question:
Paintball guns were originally developed to mark trees for logging. A forester aims his gun directly at a knothole in a tree that is 8.0 m above the gun. The base of the tree is 15 m away. The speed of the paintball as it leaves the gun is 50 m/s. How far below the knothole does the paintball strike the tree? Express your answer with the appropriate units.