Final answer:
The horizontal and vertical components of a projectile fired at 50 m/s at a 30-degree angle are 43.3 m/s and 25 m/s, respectively. These components are derived using cosine for the horizontal and sine for the vertical, along with the initial velocity and angle.
Step-by-step explanation:
The student asks to find the horizontal and vertical components of a projectile's velocity given that it is fired at an initial speed of 50 m/s at a 30-degree angle relative to the horizontal. In physics, specifically in the study of projectile motion, the horizontal and vertical components of a projectile's velocity can be determined using trigonometric functions.
To find the horizontal component (Vx), we use the formula Vx = v cos(Θ), where v is the initial velocity and Θ is the angle of launch. For a velocity of 50 m/s and an angle of 30 degrees, we apply the formula to get Vx = 50 m/s * cos(30°). Using the cosine of 30 degrees, which is 0.866, we get Vx = 43.3 m/s.
To determine the vertical component (Vy), we use the formula Vy = v sin(Θ), where again v is the initial velocity and Θ is the angle. So, Vy = 50 m/s * sin(30°). Since the sine of 30 degrees is 0.5, we find Vy = 25 m/s.
These components are crucial to understanding the behavior of a projectile in flight, and they are fundamental in calculating the trajectory, the time of flight, and the range of the projectile. The horizontal component represents the consistent velocity that influences how far the projectile will travel, while the vertical component is influenced by gravity and will determine the peak height the projectile reaches before descending back to the ground.