When a particle is projected horizontally with an initial velocity from a certain height, it follows a parabolic trajectory due to the combination of its horizontal and vertical motions.
In this case, the vertical motion of the particle can be analyzed separately. The particle is projected horizontally, so its initial vertical velocity is 0 m/s. The only force acting on the particle in the vertical direction is gravity, which causes it to accelerate downward at a rate of approximately 9.8 m/s² (neglecting air resistance).
To determine how far from the bottom of the tower the particle hits the ground, we can calculate the time it takes for the particle to fall from the top of the tower to the ground using the equation:
h = (1/2) * g * t²
Where: h is the vertical distance traveled (80.5 m) g is the acceleration due to gravity (9.8 m/s²) t is the time of flight
Rearranging the equation to solve for t:
t = sqrt(2h / g)
t = sqrt(2 * 80.5 m / 9.8 m/s²) ≈ 4.04 s
Since the horizontal velocity remains constant throughout the motion, we can find the horizontal distance traveled by multiplying the horizontal velocity (50 m/s) by the time of flight:
Distance = Horizontal Velocity * Time of Flight
Distance = 50 m/s * 4.04 s ≈ 202 m
Therefore, the particle will be approximately 202 meters from the bottom of the tower when it hits the ground.