Final answer:
The range of a projectile fired at an angle from ground level can be calculated using the horizontal component of initial speed, time of flight derived from the vertical motion, and basic kinematic equations. Given the initial speed and angle of elevation, the range formula is applied to determine the horizontal distance the projectile covers.
Step-by-step explanation:
To calculate the range of a projectile fired from ground level with an initial speed and an angle of elevation, one must use the equations of projectile motion. In this problem, there are two components of motion to consider: horizontal and vertical. The horizontal component (velocity along the x-axis) and vertical component (velocity along the y-axis) can be derived from the initial speed and angle of elevation using basic trigonometric functions.
The horizontal velocity (vx) is the initial speed (v0) multiplied by the cosine of the launch angle (θ), and the vertical velocity (vy) is the initial speed multiplied by the sine of the launch angle. The time of flight can be calculated by considering the vertical motion and using the kinematic equation that describes motion under constant acceleration (gravity), factoring in that the projectile starts and ends at the same height (ground level).
The range of the projectile is then found by multiplying the horizontal velocity by the time of flight. It can be calculated using the formula: range = vx × time of flight. The exact value can be determined by plugging the given numbers into this equation.
Note: The student's question mentions a different initial speed (450 m/sec) than the provided reference examples, so the calculation should be tailored to the actual speed provided by the student.