Having seen in Example 10. 6 that there is a simple expression for the horizontal range of a projectile across level ground, you begin to wonder whether there is an expression for the horizontal range of an object that is thrown with initial speed \(v_{1}\) at an angle \(\theta\) above the horizontal from the edge of a cliff of height \(h\).

Data from Example 10.6

How far from the launch position is the position at which the ball of Figure 10.32 is once again back in the cart? (This distance is called the horizontal range of the projectile.)

Earth reference frame