How to Calculate the Height of a Building Using Projectile Motion

Projectile motion involves the motion of an object projected into the air which then moves under the influence of gravity. In this case, we are using a soccer ball kicked by a child at an angle from the edge of a building with a known initial velocity. To determine the height of the building, we need to break down the motion of the ball into its horizontal and vertical components.

Horizontal Component

First, we calculate the horizontal component by multiplying the initial velocity of the ball by the cosine of the angle at which it was kicked. This horizontal velocity remains constant throughout the ball's flight. It helps us determine the time the ball spends in the air as it travels a known distance horizontally.

Vertical Component

Next, the vertical component is found by multiplying the initial velocity by the sine of the angle. Using the calculated time the ball is in the air, we utilize the kinematic equation y = yo + voyt - (1/2)gt² to calculate the vertical displacement of the ball. By setting the initial height as 0, we can find the height of the building where the ball was kicked.

In our scenario, the initial velocity of the soccer ball was 15 m/s at an angle of 35°. By breaking down the velocity into horizontal and vertical components, and calculating the displacement in each direction, we can determine that the height of the building is approximately 71.63 meters.

Projectile motion is a fundamental concept in physics and is commonly used to analyze the motion of objects in the air. By understanding how to break down the motion into its components, we can calculate various parameters such as height, distance, and time of flight.