I asked Copilot (Microsoft AI) just to get an initial answer (numbers used are probably total nonsense):
To calculate the horizontal distance covered by an object with a surface area of 1 square centimetre, traveling at an initial speed of 100 km/h at a 45-degree angle, we consider both the ideal case (without air resistance) and the realistic case (with air resistance).
Ideal Case (Without Air Resistance)
In the absence of air resistance, the horizontal distance ( d ) can be calculated using the formula:
d = \frac{v_0^2 \sin(2\theta)}{g}d=gv02sin(2θ)
where:
- ( v_0 ) is the initial velocity,
- ( \theta ) is the launch angle,
- ( g ) is the acceleration due to gravity (approximately ( 9.81 , \text{m/s}^2 )).
For ( v_0 = 100 , \text{km/h} ) (which is approximately ( 27.78 , \text{m/s} )) and ( \theta = 45^\circ ):
d = \frac{(27.78)^2 \sin(90^\circ)}{9.81} \approx 78.65 \, \text{meters}d=9.81(27.78)2sin(90∘)≈78.65meters
Realistic Case (With Air Resistance)
Considering air resistance, the horizontal distance is slightly reduced due to the drag force acting on the object. Using numerical integration, we find:
- Horizontal distance without air resistance: 78.65 meters
- Horizontal distance with air resistance: 77.77 meters
So, the object covers approximately
77.77 meters when air resistance is taken into account.
If you have any further questions or need additional details, feel free to ask!
