Question

You launch a shell from a cannon with an initial velocity of 950 m/s at an angle of 56.6 degrees to the horizontal at the bottom of a 153 m deep canyon. The shell continues up and out of the canyon and falls to the ground a long ways away. As you think about the work needed to calculate how far away the projectile will land and how high it will go, you realize that the cannon shell won't go anywhere near as high as you calculate it will and it won't go anywhere near as far as you calculate it will. Why is that?

Answer 1

The cannon shell won't go as high or as far as calculated due to factors such as air resistance and the curvature of the Earth. Air resistance reduces the shell's speed and alters its trajectory, while the curvature of the Earth causes the surface to lower along a horizontal line parallel to the ship, resulting in a shorter range and lower height.

Step-by-step explanation:

The reason why the cannon shell won't go as high or as far as calculated is due to various factors such as air resistance and the curvature of the Earth.

Air resistance, although assumed to be negligible in some calculations, can actually have a significant impact on the motion of the projectile.

As the shell travels through the air, it experiences drag which reduces its speed and alters its trajectory.

Additionally, the curvature of the Earth comes into play.

The assumption of a flat Earth in projectile motion calculations can lead to errors, especially over long distances.

As the shell moves farther away from the cannon, the Earth's curvature causes the surface to lower along a horizontal line parallel to the ship, resulting in a shorter range and a lower height for the projectile.