Answer:
vₓ = 6.73 m/s
Explanation:
- Assuming no other external influences than gravity, in the horizontal direction (which we make to coincide with the x- axis) , speed is constant, so, applying the definition of average velocity, we can write the following equation:
[tex]v_{x} = \frac{\Delta x}{\Delta t} (1)[/tex]
- Now, in the vertical direction (coincident with the y- axis) , as both movements are independent each other, initial velocity is zero, so we can write the following equation for the vertical displacement:
[tex]\Delta h = \frac{1}{2} * g * t^{2} (2)[/tex]
- where Δh = -37.0 m , g = -9.8 m/s2
- Solving (2) for t, we get:
[tex]t = \sqrt{\frac{2*\Delta h}{g} } =\sqrt{\frac{2*37.0m}{9.8m/s2}} = 2.75 s (3)[/tex]
- Taking t₀ = 0, ⇒ Δt = t
- Replacing (3) in (1), we get:
[tex]v_{x} = \frac{\Delta x}{\Delta t} = \frac{x}{t} = \frac{18.5m}{2.75s} = 6.73 m/s[/tex]
- As the horizontal velocity is constant, the initial horizontal velocity is just the average one, i.e., 6.73 m/s.
