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Vikki [24]
3 years ago
15

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 a

chieve 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.
Physics
2 answers:
klio [65]3 years ago
8 0

Answer:

\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}.

Assumptions:

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

Explanation:

Consider the "SUVAT" equation

\displaystyle \frac{v^{2} - u^{2}}{2a} = x,

where

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

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

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

Apply the previous equation to find the minimum height, x:

\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.

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

Natali5045456 [20]3 years ago
3 0

Answer:

0.20

0.46

0.82

1.28

1.84

Explanation:

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