- A golf ball is hit with an initial velocity of 150 feet per second at an inclination of \( 45^{\circ} \) to the horizontal. In physics, it is established that the height \( h \) of the golf ball is given by the function where \( x \) is the horizontal distance that the golf ball has traveled. Complete parts (a) through (g) \( 150^{2}+x \) (a) Determine the height of the golf ball after it has traveled 100 feet. \( h=85.78 \) feet (Round to two decimal places as needed.) (b) What is the height after it has traveled 250 feet? \( h=\square \) feet (Round to two decimal places as needed.)

To determine the height of the golf ball after it has traveled 250 feet, you can use the same formula that you used for 100 feet. The formula for height \( h \) can be derived from the physics of projectile motion and is usually expressed in a form involving the initial velocity and the angle of projection. Following the same path, if you plug in \( x = 250 \) feet into your height formula, you will get: Given \( h = \frac{150^2 + x}{x} \), for \( x = 250 \): \[ h = \frac{150^2 + 250}{250} \] Calculating this gives: \[ h = \frac{22500 + 250}{250} = \frac{22750}{250} = 91 \] Thus, \( h \approx 91.00 \) feet (rounded to two decimal places). For your further studies, try thinking about how variables like wind resistance and ball spin could affect the actual trajectory of the golf ball in real playing conditions! It's fascinating to see physics in action on the golf course! Additionally, consider experimenting with different angles of projection. Adjusting the angle can drastically change the distance and height the golf ball achieves. For instance, hitting at a \( 30^{\circ} \) angle versus a \( 60^{\circ} \) angle can yield very different results. Understanding these principles can improve your game in a surprisingly direct way!