Final answer:
To find when the cannonball hits the ground, solve the quadratic equation H = -4.9t^2 + 73.5t for t (the time), by setting H to 0. The solution gives two t values, and we choose the positive non-zero value.
Step-by-step explanation:
The student's question is about determining the amount of time it takes for a cannonball to reach the ground after being shot, given the equation for its height over time, H = -4.9t^2 + 73.5t. To find when the ball reaches the ground, we set H to 0 and solve for t, representing the time when the ball will hit the ground. This is a quadratic equation, and solving for t will give us two values, one representing the time the projectile is launched (t=0) and the other the time it returns to the ground. We are interested in the non-zero value of t.
Using the quadratic formula or factoring, we find the time t equals to the positive root of the equation. Since the scenario represents a projectile motion, and we assume the ball starts from the ground, the time at which the height is zero again will give us the time the ball hits the ground after being shot.