Let the height of a projectile above the ground be given by

where is the initial velocity in ft/sec.

- Show that the average velocity on the interval (with ) is
and that the velocity at time is

- Find the time at which velocity equals zero.
- Find the velocity of the projectile when it gets back to earth (i.e., when f(t) = 0 again).
- Find the initial velocity such that the projectile returns to earth in 1 second, 10 seconds, and in seconds.
- Prove that the projectile undergoes constant acceleration.
- Find another formula for the height such that the acceleration is a constant -20 ft/sec^2.

- The average velocity from time to time is given by
The instantaneous velocity is the limit of this as or,

- Let . This implies seconds.
- We look for the solutions of .
The solution corresponds to the time the projectile was fired. So, the projectile returns to earth at time , so evaluating at this time we have,

- If the projectiles returns in 1 second then we have
If the projectile returns in 10 seconds then we have

If the projectile returns in seconds then we have (with ),

- Acceleration is given by . This is a constant.
- Let . Then and , as requested.