Chapter 5, Problem 24A

How does the vertical distance a projectile falls below an otherwise straight-line path compare with the vertical distance it would fall from rest in the same time?

To determine

To compare: The vertical distance a projectile falling on Earth with the vertical distance of a free fall at the same time.

Answer to Problem 24A

Projectile will fall with equal acceleration and velocity and cover equal distance at comparative time falling down the Earth.

Explanation of Solution

Introduction:

Gravitational force on every object reaching towards the Earth applies equally.

Let’s say a projectile is fired down a hill. The projectile object will distribute in two components horizontal and vertical. At every point in the vertical motion, projectile will not experience any gravitational force on the horizontal component other than its momentum. But, every point on its motion reaching towards Earth, projectile will experience equal acceleration due to gravity that is $g=9.8{\text{m/s}}^{\text{2}}$ going down.

Similarly, in the vertical acceleration of the particle in free fall, acceleration due to gravity will be applied equally with the same value $g=9.8{\text{m/s}}^{\text{2}}$ . Thus, gravity of Earth will make both the projectile projected down a hill or in a free fall to fall down with the same velocity and acceleration at equal heights.

Conclusion:

Thus, while falling down either in projectile motion or vertical motion in free fall, acceleration due to gravity applied equally at the same time to both the particles.