Final answer:
In projectile motion without air resistance, the horizontal displacement after 0.5 seconds is 2.4 m and the vertical displacement (ignoring any typos in the options provided) is 2.025 m; the components of velocity remain constant horizontally and change vertically due to gravity.
Step-by-step explanation:
The question involves projectile motion in two dimensions and the concept of independent components of motion. When an object is thrown with initial horizontal and vertical components of velocity, these two motions are independent of each other. The horizontal motion has a constant velocity due to the absence of horizontal forces (ignoring air resistance), while the vertical motion is affected by gravity, which is -9.8 m/s2 in the downward direction (taking upwards as positive).
For the horizontal component, the displacement sx is calculated using the formula:
sx = vx × t
where
vx is the horizontal component of velocity (4.8 m/s) and
t is the time (0.5 s).
Hence, the horizontal displacement is:
sx = 4.8 m/s × 0.5 s = 2.4 m
For the vertical component, the displacement sy after 0.5 s under the influence of gravity (assuming downwards is negative) is calculated using the formula:
sy = vy × t + ½ a × t2
where
vy is the initial vertical component of velocity (+6.5 m/s),
t is the time (0.5 s), and
a is the acceleration due to gravity (-9.8 m/s2).
Hence, the vertical displacement is:
sy = 6.5 m/s × 0.5 s + ½ × (-9.8 m/s2) × (0.5 s)2
sy = 3.25 m - 1.225 m
sy = 2.025 m
Note that this value is positive, indicating that the object is still moving upwards at 0.5 s into its trajectory. So, the correct components of displacement after 0.5 seconds of flight are horizontal: 2.4 m, and vertical: 2.025 m. There seems to be a slight error in the options provided, as none of them match the correct answer. As such, a conversation with the student to clarify the given options or correct the question might be warranted.