Calculating the Initial Speed of a Horizontally Thrown Object from a Height

To calculate the initial speed of a horizontally thrown object from a height, we need to utilize the principles of projectile motion. In this article, we will explore the steps required to determine the initial speed of a snowball thrown horizontally from a building that is 11.0 meters high and lands 24 meters from the base.

Understanding the Problem

The problem involves a snowball thrown horizontally from the top of a building. The height of the building is given as 11.0 meters, and the snowball lands 24 meters from the base. To solve this, we need to break down the problem into components of vertical and horizontal motion.

Calculating the Time of Flight

The first step is to calculate the time of flight. This can be done using the vertical motion equation. We assume uniform acceleration due to gravity (g 9.81 m/s2) and use the formula:

s v 0 1/2gt2

Rearranging for time (t), we get:

t √(2h/g)

Substituting the given height (h 11.0 m) into the equation:

t √(2 * 11 / 9.81) √(22 / 9.81) 1.1952286 seconds

Calculating the Horizontal Speed

With the time of flight known, we can calculate the horizontal speed (U) using the horizontal distance (dh) covered by the snowball:

U dh / t

Substituting the distance (dh 24 m) and the time (t 1.1952286 s):

U 24 m / 1.1952286 s 20.14 m/s

Conclusion

The initial speed (U) of the snowball thrown horizontally from a height of 11.0 meters is approximately 20.14 m/s. This solution assumes standard gravitational acceleration and horizontal launch conditions.

Key Points to Remember

Use the vertical motion equation to find the time of flight. Utilize the horizontal distance and time of flight to calculate the initial horizontal speed. Assume constant gravity (g 9.81 m/s2) for accurate calculations.

Keywords: initial speed, horizontal throw, projectile motion