Answer:
6.53 s
Step-by-step explanation:
The height of the cannon ball is represented by a quadratic function as:
h(t) = -4.9t² + 30.5t +9.8.
At 0 s (i.e. t = 0), h(0) = -4.9(0²) + 30.5(0) + 9.8 = 9.8
That means that the cannon ball is initially at a height of 9.8 m above the ground. To calculate the time it takes the ball to touch the ground, we use:
h(t) = -4.9t² + 30.5t +9.8
It touches the ground when h(t) = 0. Hence:
0 = -4.9t² + 30.5t + 9.8
Solving the above quadratic equation gives:
t = 6.53 s and t = -0.31 s
Since the time cannot be negative, hence t = 6.53 s. Therefore it takes the ball 6.53 s to hit the ground.
