Final answer:
To determine when a ball and rock reach the same height, set their height equations equal and solve for time x, using the quadratic formula or factoring, and round to two decimal places.
Step-by-step explanation:
The student's question involves finding the time when a ball shot from a cannon and a rock thrown by Bob reach the same height. This requires equating the two equations given for the height of the ball and the rock as functions of time, y = -4x^2 + 35x + 15 and y = -5x^2 + 20x + 60, and solving for x. By setting these two equations equal to each other and simplifying, we obtain a quadratic equation, which can be solved using the quadratic formula or by factoring, if possible.
To find when the ball and the rock reach the same height, we solve the equation -4x^2 + 35x + 15 = -5x^2 + 20x + 60. By rearranging and combining like terms, we get x^2 - 15x - 45 = 0. Using either factoring or the quadratic formula, we find the solution for x that represents the time when the ball and the rock are at equal heights. We will round this solution to the nearest hundredth as per the instructions given.