91Ó°ÊÓ

Horizontal projection occurs when an object is fired or propelled along a direction parallel to the ground, without any initial vertical velocity. In this scenario, the only force acting on the object after it is projected is gravity, which affects its vertical motion. The horizontal component of motion, however, remains unaffected by gravity and is characterized by constant velocity. For the given problem, the ball was projected with a horizontal speed of 20 m/s. This speed does not change during its travel, as there are no horizontal forces acting on it to either speed up or slow it down. This aspect of horizontal projection helps in predicting the horizontal distance covered by projectiles accurately since it depends solely on the initial horizontal speed and the time of flight.

While the object moves horizontally, its vertical motion is influenced by gravity. This means the ball will accelerate downwards at a rate equal to the gravitational acceleration, which is typically denoted by the symbol \( g \). In most calculations, \( g \) is approximated to \( 9.8 \, \mathrm{m/s^2} \), but for simplicity, it was taken as \( 10 \, \mathrm{m/s^2} \) in this exercise.Since the ball was initially projected horizontally, its initial vertical velocity is \( 0 \, \mathrm{m/s} \). As it falls under gravity, the vertical motion of the ball can be described by the equation:- \[ h = \frac{1}{2}gt^2 \]- By substituting the known values, the time taken to reach the ground was calculated as approximately 4.47 seconds.Understanding vertical motion is crucial because it determines how long the projectile remains in the air and the velocity it gains as it falls.

Free fall refers to the motion of an object under the influence of gravitational force only. In this scenario, our ball, once projected horizontally, experiences free fall where gravity pulls it towards the earth.In free fall, the vertical distance the object travels can be determined using the equation:- \[ h = \frac{1}{2}gt^2 \]- Using this formula, we found out that the ball takes approximately 4.47 seconds to reach the ground from a height of 100 meters. In free fall, it’s crucial to remember that air resistance is typically ignored, implying that in a perfect scenario, only gravity acts on the object. This simplifies calculations and helps us predict outcomes more accurately.

Calculating the final velocity with which a projectile strikes the ground involves combining both horizontal and vertical velocity components into a single resultant velocity.- **Horizontal Component**: The horizontal velocity remains constant at \( 20 \, \mathrm{m/s} \), as we assume no air resistance.- **Vertical Component**: As the ball falls, gravity increases its vertical velocity to approximately \( 44.7 \, \mathrm{m/s} \).To find the total velocity when the ball hits the ground, we use the Pythagorean theorem:- \[ v = \sqrt{v_x^2 + v_y^2} \]- After calculating the values, we find the ball strikes the ground with a speed of approximately \( 48.33 \, \mathrm{m/s} \). Understanding how to break down and calculate each component of velocity is essential for predicting exactly where and how an object will land.