A ball is dropped from $a$ height of 49 m. The quadratic equation $d(t)=-t^2+49$ provides information about the height of the ball d, after $t$ seconds. In how many seconds, does the ball hit the ground?

Step 1 (Formulate the Condition): The ball hits the ground when its height $d(t)$ is exactly $0$ meters.

Step 2 (Set up the Equation): Using the given equation $d(t)=-t^2+49$:

Step 3 (Solve for t): Taking the square root of both sides:

Since time $t$ represents elapsed physical seconds, it must be non-negative ($t\ge 0$). Thus, we discard $t=-7$.

Step 4 (Conclusion): The ball hits the ground in exactly 7 seconds.