A projectile is launched horizontally with an initial velocity of 20 m/s. What is the projectile's horizontal velocity 2 seconds later, assuming negligible air resistance?

Understand the Problem

The question is asking for the horizontal velocity of a projectile after a certain time, given that it is launched horizontally and we are assuming negligible air resistance. Since horizontal velocity does not change in the absence of air resistance, we will conclude that the horizontal velocity remains constant.

Answer

The horizontal velocity remains $v_{0x}$.

Steps to Solve

Identify the horizontal velocity The horizontal velocity of a projectile launched horizontally remains constant. Therefore, we need the initial horizontal velocity, denoted as $v_{0x}$.
Review the time of flight Since we are to find the velocity after a certain time ( t ), we check the given time to ensure it's associated with the horizontal motion.
Calculate the horizontal velocity after time ( t ) Since the horizontal component of velocity does not change due to air resistance, after time ( t ) the horizontal velocity is still $v_{0x}$.
Write the final expression The expression for the horizontal velocity after time ( t ) is simply:

$$ v_x(t) = v_{0x} $$

where $v_{0x}$ is the initial horizontal velocity.

The horizontal velocity after time ( t ) remains $v_{0x}$.

More Information

In projectile motion without air resistance, the horizontal velocity does not change over time, which makes calculations straightforward. The only assumption is that the initial horizontal velocity is given.

Tips

Confusing horizontal and vertical velocities: Remember, horizontal velocity does not change during flight, while vertical velocity is influenced by gravity.
Ignoring air resistance too early: Always confirm that the problem states that air resistance is negligible, which allows us to not consider its effect.

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