Question

The height (in meters) of a shot cannonball follows a trajectory given by $h(t) = -4.9t^2 14t - 0.4$ at time $t$ (in seconds). for how many seconds is the height of the cannonball at least $6$ meters?

Answer 1

The height of the cannonball is at least 6 meters for 1.21 ≤ t ≤ 2.89 seconds.

Step-by-step explanation:

To find the time for which the height of the cannonball is at least 6 meters, we can set up the given equation:

-4.9t^2 + 14t - 0.4 ≥ 6

Re-arranging the equation, we have:

-4.9t^2 + 14t - 6.4 ≥ 0

To solve this quadratic inequality, we can factor or use the quadratic formula. Let's solve it using the quadratic formula:

The values of t that satisfy the inequality are approximately t ≥ 1.21 and t ≤ 2.89.

Therefore, the height of the cannonball is at least 6 meters for 1.21 ≤ t ≤ 2.89 seconds.