## Exploration 3.5: Uphill and Downhill Projectile Motion

Please wait for the animation to completely load.

A projectile is launched at t = 0 s (**position is given in meters and time is given in seconds**). You may change the projectile's launch angle and initial speed and the height of the hill by using the text boxes and clicking the "set values and play" button. Restart.

For h = 0 m, vary the projectile's launch angle and initial speed and consider the following questions.

- For a given initial speed, what launch angle will provide the maximum range of the projectile?
- For the value of launch angle in (a), what is the value of the initial speed that will hit the target?
- What other value(s) of the projectile's launch angle and initial speed will enable the projectile to hit the target?
- Are these values unique?
- What is the general relationship between launch angle and initial speed?

For h = 10 m, vary the projectile's launch angle and initial speed and consider the following questions.

- For a given initial speed, what launch angle will provide the maximum horizontal displacement of the projectile?
- What value(s) of the projectile's launch angle and initial speed will enable the projectile to hit the target?
- Are these values unique?
- Are these values the same as in (c)?

For h = -10 m, vary the projectile's launch angle and initial speed and consider the following questions.

- For a given initial speed, what launch angle will provide the maximum horizontal displacement of the projectile?
- What value(s) of the projectile's launch angle and initial speed will enable the projectile to hit the target?
- Are these values unique?
- Are these values the same as in (c) and (g)?