Answer:
[tex]\large \boxed{\text{b. 9.4 m}}[/tex]
Explanation:
1. Break down the velocity into its horizontal and vertical components
[tex]\cos 20^{\circ} = \dfrac{v_{\text{h}}}{12} = 0.9397\\\\v_{\text{h}} = \text{11.3 m/s}[/tex]
[tex]\sin 20 = \dfrac{v_{\text{v}}}{12} = 0.3420\\\\v_{\text{v}} = \text{4.10 m/s}[/tex]
2. Calculate the time of flight
Use the vertical component of velocity to calculate the time to the height of the jump.
[tex]v = gt\\t = \dfrac{v}{g} = \dfrac{\text{4.10 m$\cdot$ s}^{-1}}{\text{9.807 m$\cdot$ s}^{-2}}= \text{0.419 s}[/tex]
It will take the same time to reach the ground.
Thus,
Time of flight = 2t = 2 × 0.419 s = 0.837 s
3. Calculate the horizontal distance
s = vt = 11.3 m·s⁻¹ × 0.837 s = 9.4 m
[tex]\text{Her horizontal displacement is $\large \boxed{\textbf{9.4 m}}$}[/tex]
