The equation y = -6t^2 - 10t + 56 describes the height (in feet) of a ball thrown downward at 10 feet per second from a height of 56 feet from the surface from Mars. In how many seconds will the ball hit the ground? Express your answer as a decimal rounded to the nearest hundredth.
The ball will hit the ground when y = 0. Solving for t in the equation y = -6t^2 - 10t + 56, we get:
-6t^2 - 10t + 56 = 0
We can factor this equation as:
(2t - 7)(3t - 8) = 0
Solving for t, we get:
t = 7/2 or 8/3
The smaller of these two values is 7/2. Therefore, the ball will hit the ground in \(\boxed{3.50}\) seconds.
