To solve these problems, we will calculate the average velocity for each given time interval using the formula for average velocity:

$\text{Average Velocity} = \frac{s(t_2) - s(t_1)}{t_2 - t_1}$

where $s(t)$ is the height function, and $t_1$ and $t_2$ are the times.

Given the height function on Mars: $s(t) = 10t - 1.86t^2$

1. Average Velocity from $t = 1$ to $t = 2$:

$\text{Average Velocity} = \frac{s(2) - s(1)}{2 - 1}$

First, calculate $s(2)$ and $s(1)$: $s(2) = 10(2) - 1.86(2^2) = 20 - 7.44 = 12.56 \text{ meters}$ $s(1) = 10(1) - 1.86(1^2) = 10 - 1.86 = 8.14 \text{ meters}$ Now, calculate the average velocity: $\text{Average Velocity} = \frac{12.56 - 8.14}{2 - 1} = \frac{4.42}{1} = 4.42 \text{ m/s}$

2. Average Velocity from $t = 1.9$ to $t = 2$:

$\text{Average Velocity} = \frac{s(2) - s(1.9)}{2 - 1.9}$

First, calculate $s(1.9)$: $s(1.9) = 10(1.9) - 1.86(1.9^2)$

Now, compute $s(1.9)$: $s(1.9) = 19 - 6.72186 = 12.27814 \text{ meters}$ Now, calculate the average velocity: $\text{Average Velocity} = \frac{12.56 - 12.27814}{2 - 1.9} = 2.81860 \text{ m/s}$

3. Average Velocity from $t = 1.99$ to $t = 2$:

Compute (s(1.999) \text{ meters}