It is true to say that a ball will land at the same time, regardless of whether it is dropped straight down from the top of a tower or thrown horizontally (assuming we neglect air resistance).
The key concept here is that, neglecting air resistance, the horizontal and vertical motions of the ball are independent of each other. When the ball is dropped straight down, it accelerates only in the vertical direction due to the force of gravity. When the ball is thrown horizontally, it also experiences the force of gravity pulling it vertically downward, but it also has an initial horizontal velocity.
Since the vertical motion is independent of the horizontal motion, the ball takes the same amount of time to fall vertically to the ground in both cases. The horizontal motion does not affect the time it takes for the ball to fall.
To illustrate this, consider two scenarios:
Dropping the ball straight down: The ball accelerates downward due to gravity, and its initial horizontal velocity is zero. The only force acting on the ball is gravity, which causes it to fall vertically downward. It will take the same amount of time to reach the ground as any other object dropped from the same height.
Throwing the ball horizontally: In this case, the ball has an initial horizontal velocity, but it still experiences the same vertical acceleration due to gravity. The horizontal motion does not affect the vertical motion or the time it takes for the ball to fall. Therefore, the ball will still take the same amount of time to reach the ground as in the first scenario.
Again, it's important to note that these statements assume negligible air resistance. In reality, air resistance can have an impact on the motion of objects, especially when considering objects with a large surface area or high velocities. However, for most common scenarios involving everyday objects, the effect of air resistance is relatively small and can often be neglected.