Final answer:
The component of the weight of the box along the inclined surface is calculated using the box's weight and the sine of the angle of the slope. The ball's acceleration in the vertical direction is -9.8 m/s², which is the acceleration due to gravity.
Step-by-step explanation:
To find the component of the weight of the box along the surface, we need to consider the gravitational force acting on the box and the slope of the inclined surface. The gravitational force on the box is mg, where m is the mass of the box (14 kg) and g is the acceleration due to gravity (9.8 m/s2). We can decompose this force into components perpendicular and parallel to the inclined surface. The component of the weight parallel to the slope (w\|) is w\| = mg\sin(\theta), where \(\theta\) is the angle of inclination (52 degrees). Plugging in the numbers: w\| = 14 kg · 9.8 m/s2 · sin(52°).
The ball's acceleration in the vertical direction as it flies through the air is constant and is due to the force of gravity. Regardless of the initial velocity or the angle of projection, the vertical acceleration is -9.8 m/s2 (negative sign indicating downward acceleration).