Final answer:
The projectile's horizontal distance can be calculated using projectile motion formulas by first resolving the initial velocity into horizontal and vertical components, then finding the time of flight and multiplying it by the horizontal velocity component to find the range.
Step-by-step explanation:
To calculate how far the object lands from where it started, projectile motion equations are needed. To find the horizontal distance, first, we have to resolve the initial velocity into its horizontal and vertical components. The horizontal velocity, Vx, is given by Vx = V*cos(θ), while the vertical velocity, Vy, is given by Vy = V*sin(θ), where V is the initial velocity and θ is the launch angle.
Using the initial velocity of 5.40 m/s and an angle of 30.0°, the horizontal velocity becomes:
Vx = 5.40 m/s * cos(30.0°)
For simplicity, assuming no air resistance and that the acceleration due to gravity is 9.81 m/s², the time of flight until the projectile lands can be deduced from the vertical motion. The time, t, it takes to reach the maximum height and fall back down is given by t = (2 * Vy) / g. The horizontal distance, or range, is then Vx * t.
Calculating the range:
Vy = 5.40 m/s * sin(30.0°)
t = (2 * Vy) / 9.81 m/s²
Range = Vx * t
Remember, the final answer will depend on the actual calculations of component velocities, the time of flight, and the resulting range.