To find the final velocity of a ball thrown downward, we can use the following kinematic equation under constant acceleration:

$v_f = v_i + a t$

Where:

• $v_f$ is the final velocity (which we're solving for),
• $v_i = 4.0 \, \text{m/s}$ is the initial velocity (the ball is thrown downward),
• $a = 9.8 \, \text{m/s}^2$ is the acceleration due to gravity,
• $t = 9.74 \, \text{seconds}$ is the time it takes to hit the ground.

Now, substituting the known values:

$v_f = 4.0 \, \text{m/s} + (9.8 \, \text{m/s}^2) \times 9.74 \, \text{s}$

Let me calculate this for you.The final velocity of the ball is approximately $99.45 \, \text{m/s}$.

Thus, the closest option is:

f. 99 m/s

Would you like more details or have any further questions?

Here are 5 related questions to deepen your understanding:

1. What would happen if the initial velocity were zero?
2. How would the final velocity change if the ball were thrown upwards instead?
3. What role does air resistance play in determining final velocity in real-world situations?
4. How would the final velocity change if the time to hit the ground were different?
5. Can we calculate the height of the building using the time and gravity?

Tip: When solving kinematics problems, always keep track of the direction of velocities and accelerations, as signs (+ or -) are crucial.