Question

A ball is thrown into the air and its position is given by h(t)= -2.9t² 93t 22 where h is the height of the ball in meters t seconds after it has been thrown. find the maximum height reached by the ball and the time at which that happens.

Answer 1

The maximum height reached by the ball is 484.12 meters, and it occurs at 15.98 seconds.

Step-by-step explanation:

The maximum height reached by the ball can be found by determining the vertex of the parabolic function representing its height. The vertex of a parabola given by the equation h(t) = -2.9t² + 93t + 22 is given by the formula t = -b/2a, where a = -2.9 and b = 93 in this case. Using this formula, we find that t = -93/(2*(-2.9)) = 15.98 seconds. To find the height at this time, we substitute the value of t into the equation: h(15.98) = -2.9(15.98)² + 93(15.98) + 22 = 484.12 meters.

The maximum height reached by the ball is therefore 484.12 meters. The time at which this occurs is 15.98 seconds.