Final answer:
To calculate the time it takes for an object to hit the ground when thrown vertically downward, use the equation t = sqrt((2h)/g), where h is the height, u is the initial velocity, g is the acceleration due to gravity, and t is the time. In this case, it will take approximately 1.56 seconds for the object to hit the ground.
Step-by-step explanation:
To calculate the time it takes for an object to hit the ground when thrown vertically downward, we need to use the equations of motion for free fall. The equation we can use is:
h = ut + 0.5gt^2
Where h is the height, u is the initial velocity, g is the acceleration due to gravity, and t is the time. Rearranging the equation, we get:
t = sqrt((2h)/g)
In this case, the height is 12 m and the initial velocity is 3.2 m/s. The acceleration due to gravity is approximately 9.8 m/s^2. Substituting these values into the equation, we get:
t = sqrt((2 * 12)/9.8) = sqrt(24/9.8) = sqrt(2.45) ≈ 1.56 s
Therefore, it will take approximately 1.56 seconds for the object to hit the ground.