Question

The height of a projectile fired upward is given by the formula s = v0t − 16t2, where s is the height, v0 is the initial velocity, and t is the time. Find the time for a projectile to return to Earth if it has an initial velocity of 280 ft/s.

Answer 1

Set s = 0 and solve 0 = v0 t − 16 t^2 with v0 = 280:

0 = 280t − 16t^2 = t(280 − 16t).

Solutions: t = 0 (launch) or 280 − 16t = 0 → t = 280/16 = 17.5 seconds.

So the projectile returns to Earth after 17.5 s.