Maximum Height of Projectile Fired at 50 m/s, 30 Degrees Above Horizontal

What is the maximum height reached by a projectile fired at an initial speed of 50 m/s, at an angle of 30 degrees above the horizontal?

Options: 1) 64 2) 96 3) 32 4) 126 5) 300

Answer:

The maximum height reached by a projectile fired at an initial speed of 50 m/s, at an angle of 30 degrees above the horizontal, is about 32 meters.

Let's dive into the world of Physics and explore the fascinating realm of projectile motion! When an object is launched into the air at an angle to the horizontal, it follows a curved path known as projectile motion. One of the key parameters to analyze in projectile motion is the maximum height that the object reaches.

To determine the maximum height reached by the projectile in this scenario, we can utilize the projectile motion equations. Specifically, we can use the equation for the maximum height reached by a projectile launched at an angle with an initial speed v, given by:

H = (v²sin²) / (2g)

Where:

- H is the maximum height

- v is the initial speed of the projectile (50 m/s in this case)

- is the launch angle (30 degrees above the horizontal)

- g is the acceleration due to gravity (approximately 9.81 m/s²)

Substituting the given values into the formula, we get:

H = (50²sin²30) / (2*9.81)

Calculating this expression, we find that the maximum height reached by the projectile is approximately 32 meters.

This calculation showcases the application of trigonometry and physics principles in analyzing projectile motion scenarios. Understanding such concepts not only helps us solve specific problems but also deepens our comprehension of the physical world around us. Projectile motion is a fundamental topic in physics, offering valuable insights into the behavior of objects in motion under the influence of gravity.