Figure 3.9 shows an airplane moving horizontally with a constant velocity of +115 m/s at an altitude of 1050 m. The directions to the right and upward have been chosen as the positive directions. The plane releases a “care package” that falls to the ground along a curved trajectory. Ignoring air resistance, determine the time required for the package to hit the ground.

Figure 3.9  The package falling from the plane is an example of projectile motion, as Examples 2 and 3 discuss.

Reasoning  The time required for the package to hit the ground is the time it takes for the package to fall through a vertical distance of 1050 m. In falling, it moves to the right, as well as downward, but these two parts of the motion occur independently. Therefore, we can focus solely on the vertical part. We note that the package is moving initially in the horizontal or x direction, not in the y direction, so that v_0y=0 m/s. Furthermore, when the package hits the ground, the y component of its displacement is y=–1050 m, as the drawing shows. The acceleration is that due to gravity, so a_y=–9.80 m/s². These data are summarized as follows:

Solution Since v_0y=0 m/s, it follows from Equation 3.5b that and