Final answer:
An object projected horizontally from a cliff will hit the ground at the same time as if it were simply dropped, because gravity acts in the vertical direction and the horizontal motion does not affect the time to fall.
Step-by-step explanation:
When an object is projected horizontally from a cliff, the time it takes to hit the ground is c. the same amount of time as if it were just dropped. This is because the horizontal component of the projectile's velocity does not affect the time it takes to fall due to gravity, which acts only in the vertical direction. According to physics principles in projectile motion, the downward acceleration due to gravity is constant and acts independently of any horizontal motion. Therefore, if two objects are dropped from the same height, one being projected horizontally and one being dropped straight down, they will both reach the ground at the same time, provided air resistance is negligible.
To understand this concept better, imagine two balls being released from the same height: one simply falls downward, while the other is thrown horizontally. If we ignore air resistance, both balls will accelerate toward the ground at the same rate due to gravity and thus take the same amount of time to reach the ground. This idea is often represented in physics textbooks using diagrams that show projectiles having the same vertical position over time, regardless of their horizontal velocity.