Sure! To determine the final velocity of the monkey, we need to follow a step-by-step approach using physics principles, specifically kinematic equations.
### Step-by-Step Solution:
1. Identify the given values:
- Initial velocity ([tex]\(u\)[/tex]): 1.24 m/s
- Distance traveled ([tex]\(s\)[/tex]): 6.71 meters
- Time taken ([tex]\(t\)[/tex]): 4.55 seconds
2. Use the kinematic equation to find the acceleration ([tex]\(a\)[/tex]):
The equation relating distance, initial velocity, acceleration, and time is:
[tex]\[
s = ut + \frac{1}{2} a t^2
\][/tex]
Substitute the known values into the equation:
[tex]\[
6.71 = (1.24 \cdot 4.55) + \frac{1}{2} a (4.55)^2
\][/tex]
3. Calculate the initial velocity component:
[tex]\[
(1.24 \times 4.55) = 5.642
\][/tex]
4. Isolate the term involving acceleration:
[tex]\[
6.71 - 5.642 = \frac{1}{2} a (4.55)^2
\][/tex]
[tex]\[
1.068 = \frac{1}{2} a (20.7025)
\][/tex]
5. Solve for acceleration ([tex]\(a\)[/tex]):
[tex]\[
1.068 = 10.35125a
\][/tex]
[tex]\[
a = \frac{1.068}{10.35125} = 0.103
\][/tex]
6. Use the final velocity equation to find the final velocity ([tex]\(v_f\)[/tex]):
The equation relating final velocity, initial velocity, acceleration, and time is:
[tex]\[
v_f = u + a t
\][/tex]
Substitute the known values:
[tex]\[
v_f = 1.24 + (0.103 \times 4.55)
\][/tex]
7. Calculate the final velocity:
[tex]\[
v_f = 1.24 + 0.469
\][/tex]
[tex]\[
v_f = 1.709
\][/tex]
Therefore, the final velocity of the monkey is [tex]\(1.709 \, \text{m/s}\)[/tex].
