The final velocity of a projectile after it travels a distance of 100 meters depends on various factors, such as the initial velocity, the angle of projection, and the presence of external forces like air resistance. I'll provide a simplified answer assuming ideal projectile motion without air resistance.
In ideal projectile motion, the horizontal and vertical motions of the projectile are considered separately. The horizontal velocity remains constant throughout the motion, while the vertical velocity changes due to the acceleration due to gravity.
Assuming the projectile is launched horizontally (angle of projection = 0 degrees) and neglecting air resistance, the horizontal velocity (Vx) remains constant. Therefore, the final horizontal velocity will be the same as the initial horizontal velocity.
However, the vertical motion is influenced by gravity. The final vertical velocity (Vy) can be determined using the equation:
Vy = V0y + gt
where V0y is the initial vertical velocity, g is the acceleration due to gravity (approximately 9.8 m/s²), and t is the time taken to travel the distance of 100 meters vertically.
To find the time of flight, we can use the equation:
s = V0y * t + (1/2) * g * t^2
Since the initial vertical velocity is usually assumed to be zero when launched horizontally, the equation simplifies to:
100 = (1/2) * g * t^2
Solving for t, we find:
t = sqrt((2 * 100) / g)
Now, we can substitute this value of t into the equation for Vy:
Vy = g * t
Thus, the final vertical velocity (Vy) after traveling 100 meters horizontally will be g * t.
Note that if the projectile is launched at an angle, the calculation becomes more complex, involving trigonometric functions and the initial velocity components in the horizontal and vertical directions.
Remember that this answer assumes ideal projectile motion without considering air resistance, which can have a significant impact on the final velocity in real-world scenarios.