To find the horizontal range an object has traveled at its maximum height, you can use the formula for the range of projectile motion. The horizontal range is the horizontal distance covered by the object before it returns to the same vertical level as its initial position.
The formula for the horizontal range (R) of projectile motion is given by:
R = (u^2 * sin(2θ)) / g
Where:
- R is the horizontal range
- u is the initial velocity (magnitude)
- θ is the angle of projection
- g is the acceleration due to gravity (approximately 9.8 m/s²)
However, in your question, you mentioned finding the horizontal range at the object's maximum height. At maximum height, the object reaches its peak and returns to the same vertical level as its initial position. At this point, the angle of projection (θ) becomes 45 degrees (assuming symmetric projectile motion).
Using this information, we can simplify the formula for the horizontal range at maximum height:
R_max_height = (u^2 * sin(2θ)) / g = (u^2 * sin(90°)) / g [Since θ = 45°] = (u^2 * 1) / g = u^2 / g
Therefore, to find the horizontal range at maximum height, you can use the formula R_max_height = u^2 / g, where u is the initial velocity and g is the acceleration due to gravity.