91Ó°ÊÓ

When an object is hurled into the air and moves under the influence of gravity alone, without any propulsion, this motion is called projectile motion. It involves the movement in two dimensions: horizontal and vertical. Important to remember is that these two components are independent of each other, meaning:

• The horizontal motion does not change because no horizontal force (like air resistance) is acting on the object.
• The vertical motion is affected by gravity, which continually accelerates the object downward.

In the provided example, both Wendy and Bill experience projectile motion. They start at the edge of the falls with a horizontal velocity and continue downwards because of Earth’s gravitational pull. The time they take to hit the bottom is the same, as gravity is the only force acting on them vertically.

Horizontal velocity refers to the speed and direction of an object moving along the horizontal axis. It is crucial in projectile motion because it remains constant throughout the object’s flight, assuming no forces act against it, such as air resistance. In our exercise, Wendy's initial horizontal velocity is 30 km/hr, given by the speed of the river. Since there's no air resistance mentioned, this velocity remains unchanged, even at the moment of impact. For Bill, his horizontal velocity is 40 km/hr (30 km/hr from the river speed plus a 10 km/hr boost from paddling). This velocity also remains steady as he descends over the falls. Such constancy makes calculations straightforward, as we need not account for any horizontal deceleration.

Gravity is a natural force that pulls objects towards Earth’s center. In projectile motion, gravity only affects the vertical component of an object's motion, giving it a downward acceleration of approximately 9.8 m/s². This vertical acceleration is why both Wendy and Bill eventually hit the ground, regardless of their initial horizontal speeds. In the scenario at Niagara Falls, gravity acts solely on the vertical motions of Wendy and Bill, meaning it is the reason they fall. Importantly, since their initial vertical velocities are zero, and gravity works uniformly without any horizontal influence, both will take the same time to reach the bottom of the falls. This concept comes into play when we need to predict how fast they will be moving overall at the moment of impact.

In physics, splitting velocity into components helps us analyze motion more effectively. We generally divide velocity into:

• Horizontal Component: This is the constant speed parallel to the ground, unaffected by gravity in ideal conditions.
• Vertical Component: This changes due to gravity, usually starting at zero when an object begins its fall, and increasing as it approaches the ground.

For the daredevils' fall, Wendy starts with a horizontal component of 30 km/hr and Bill with 40 km/hr. As both go over the falls, their initial vertical velocity is zero. As they descend, gravity increases their vertical speed, contributing to the total speed they hit the ground with. At impact, Bill’s greater horizontal velocity means he is moving faster compared to Wendy, highlighting how initial velocity components influence final speeds in projectile motion.