jmc

Question

The equation y = -4.9t^2 + 23.8t describes the height (in meters) of a projectile launched from the ground at 23.8 meters per second. In how many seconds will the projectile first reach 28 meters in height?

Accepted Answer

Setting y to 28, we find the following: align* 28& = -4.9t^2 + 23.8t 0 & = -4.9t^2 + 23.8t - 28 0 & = 49t^2 - 238t + 280 & = 7t^2 - 34t + 40 & = (7t - 20)(t - 2) align*Our possible values for t are 207 2.857 or 2. Of these, we choose the smaller t, or 2.