To find the maximum height reached by the object, we can use kinematic equations. Here's how we approach the problem:

Key Information:

• The total time of flight is 3 seconds.
• The object was launched vertically, so the motion is along a straight line.
• The acceleration due to gravity, $g$, is $9.8 \, \text{m/s}^2$, and it's acting downward.

Step-by-Step Solution:

1. Time to reach the maximum height: The object reaches its maximum height halfway through its total time of flight. Therefore, the time to reach the maximum height is: $t_{\text{up}} = \frac{t_{\text{total}}}{2} = \frac{3}{2} = 1.5 \, \text{seconds}.$

2. Initial velocity ($v_0$): We use the following kinematic equation for vertical motion, where at maximum height, the final velocity ($v$) is 0: $v = v_0 - g t.$ At maximum height, $v = 0$, so we solve for $v_0$: $0 = v_0 - 9.8 \times 1.5.$ $v_0 = 9.8 \times 1.5 = 14.7 \, \text{m/s}.$ So, the initial velocity is 14.7 m/s.

3. Maximum height ($h_{\text{max}}$): We use the following kinematic equation to find the maximum height: $h_{\text{max}} = v_0 t_{\text{up}} - \frac{1}{2} g t_{\text{up}}^2.$ Substituting the values: $h_{\text{max}} = 14.7 \times 1.5 - \frac{1}{2} \times 9.8 \times (1.5)^2.$ $h_{\text{max}} = 22.05 - 11.025 = 11.025 \, \text{meters}.$

Final Answer:

The maximum height reached by the object is 11.025 meters.

Would you like more details or have any questions?

Here are some related questions to further your understanding:

1. What is the time taken for the object to hit the ground after reaching maximum height?
2. How can the equation for motion be modified for an object thrown at an angle?
3. What would the maximum height be if the object was launched with a higher initial velocity?
4. How does the acceleration due to gravity affect the time to reach maximum height?
5. Can you calculate the total velocity of the object just before hitting the ground?

Tip: For problems involving vertical motion, always remember that the total flight time is symmetrical around the maximum height if the object is launched and lands at the same height.