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To achieve a speed of 2 m/s, the bottle must be dropped at m. To achieve a speed of 3 m/s, the bottle must be dropped at m. To achieve a speed of 4 m/s, the bottle must be dropped at m. To achieve a speed of 5 m/s, the bottle must be dropped at m. To achieve a speed of 6 m/s, the bottle must be dropped at m.

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jacob193

Answer:

[tex]\begin{array}{l|l}\text{Speed}\; \mathrm{(m\cdot s^{-1})} & \text{Minimum Height\;(m)}\\\cline{1-2}\\[-1em] 2 & 0.204\\3&0.459\\4 & 0.815\\5 & 1.27 \\6 & 1.83\end{array}[/tex].

Assumptions:

  • The object is dropped in a free fall.
  • There's no air resistance.
  • The downward acceleration due to gravity is [tex]\rm 9.81\;m\cdot s^{-2}[/tex]

Explanation:

Consider the "SUVAT" equation

[tex]\displaystyle \frac{v^{2} - u^{2}}{2a} = x[/tex],

where

  • [tex]v[/tex] is the final velocity,
  • [tex]u[/tex] is the initial velocity,
  • [tex]a[/tex] is the acceleration of the object, and
  • [tex]x[/tex] is the change in the object's position.

For example, if the bottle needs to achieve a speed of [tex]v = \rm 2\; m\cdot s^{-1}[/tex] by the time it reaches the ground,

  • [tex]u = 0[/tex] since the statement that the bottle is "dropped" implies a free fall.
  • [tex]a = g = \rm 9.81\;m\cdot s^{-2}[/tex].

Apply the previous equation to find the minimum height, [tex]x[/tex]:

[tex]\displaystyle x = \frac{v^{2} - u^{2}}{2a} = \rm \frac{\left(2\; m\cdot s^{-1}\right)^{2}}{2\times 9.81\; m\cdot s^{-2}} \approx 0.204\; m[/tex].

Replace the [tex]v[/tex] value and apply the formula to find the minimum height required to reach different final speeds.

oliviac5670spam

Answer:

To achieve a speed of 2 m/s, the bottle must be dropped at  

✔ 0.20

m.

To achieve a speed of 3 m/s, the bottle must be dropped at  

✔ 0.46

m.

To achieve a speed of 4 m/s, the bottle must be dropped at  

✔ 0.82

m.

To achieve a speed of 5 m/s, the bottle must be dropped at  

✔ 1.28

m.

To achieve a speed of 6 m/s, the bottle must be dropped at  

✔ 1.84

m.

Explanation: