Projectile Motion: How Long Will the Ball Be in the Air?

Understanding Projectile Motion

Projectile motion is a form of motion experienced by an object that is projected into the air. It follows a curved path under the influence of gravity without any additional propulsion after its initial launch.

Finding Time in the Air and Horizontal Distance Traveled

Given: Initial velocity of 200 m/s and launch angle of 38 degrees

Final Answer: The ball will be in the air for approximately 20.27 seconds and will travel a horizontal distance of approximately 527.05 meters.

Explanation

In this question, we are given the initial velocity of a ball and the angle at which it is launched. To find how long the ball will be in the air, we need to use the formula for the time of flight of a projectile. The formula is:

t = (2 * u * sinθ) / g

Where t is the time, u is the initial velocity, θ is the launch angle, and g is the acceleration due to gravity.

Next, to find the horizontal distance, we need to use the formula for the range of a projectile. The formula is:

R = (u^2 * sin(2θ)) / g

Where R is the range.

Substituting the given values into the formulas, we get:

t = (2 * 200 * sin(38°)) / 9.8 ≈ 20.27 seconds

R = (200^2 * sin(2 * 38°)) / 9.8 ≈ 527.05 meters

Therefore, the ball will be in the air for approximately 20.27 seconds and will travel a horizontal distance of approximately 527.05 meters.