The equation y = -16t^2 + 26t + 105 describes the height (in feet) of a ball tossed up in the air at 26 feet per second from a height of 105 above the ground. In how many seconds will the ball hit the ground? express your answer as a decimal rounded to the nearest tenth.

Answer 1

To find out when the ball will hit the ground, we need to find the time when the height (y) is equal to 0.

Setting y = 0 in the equation, we get:

0 = -16t^2 + 26t + 105

This is a quadratic equation that can be solved using the quadratic formula:

t = (-26 ± √(26^2 - 4(-16)(105))) / (2(-16))

t = (-26 ± √(676 + 6720)) / (-32)

t = (-26 ± √7396) / (-32)

t = (-26 ± 86) / (-32)

Now we have two possible solutions:

t = (-26 + 86) / -32 = 60 / -32 = -1.875

t = (-26 - 86) / -32 = -112 / -32 = 3.5

The positive solution, 3.5 seconds, is the time it takes for the ball to hit the ground.