To determine the horizontal displacement of the biker, we'll break down the problem into several steps:
1. Identify the speed of the biker and the duration of travel:
- Speed of the biker: [tex]\( 2.0 \, \text{meters/second} \)[/tex]
- Time of travel: [tex]\( 60 \, \text{seconds} \)[/tex]
2. Understand the inclination and identify the angle:
- Angle of the road with the horizontal: [tex]\( 15.0^\circ \)[/tex]
3. Calculate the horizontal component of the biker's speed:
The biker's speed is at an angle to the horizontal, so we need the horizontal component of his speed. This component can be found using the cosine function:
[tex]\[
\text{Horizontal speed} = \text{Speed} \times \cos(\theta)
\][/tex]
where [tex]\( \theta \)[/tex] is the angle of inclination ([tex]\( 15.0^\circ \)[/tex]).
Thus, we get:
[tex]\[
\text{Horizontal speed} \approx 2.0 \times \cos(15.0^\circ) \approx 1.9318516525781366 \, \text{meters/second}
\][/tex]
4. Calculate the total horizontal displacement:
The horizontal displacement can then be found by multiplying the horizontal speed by the time of travel:
[tex]\[
\text{Horizontal displacement} = \text{Horizontal speed} \times \text{Time}
\][/tex]
Substituting the values, we get:
[tex]\[
\text{Horizontal displacement} \approx 1.9318516525781366 \, \text{meters/second} \times 60 \, \text{seconds} \approx 115.9110991546882 \, \text{meters}
\][/tex]
Thus, the horizontal displacement of the biker is approximately [tex]\(115.911 \, \text{meters}\)[/tex].
