Physics, 03.07.2019 07:10 aleshachrishon42

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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Answer from: hh23135

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

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

is the final velocity,

is the initial velocity,

is the acceleration of the object, and

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,

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, :

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

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

Answer from: Quest

b. latent learning (the word "latent" itself means something that exists but isn't obvious, only under certain conditions! )

Answer from: Quest

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

$f\alpha \frac{dp}{dt}$

⇒ $f= k \frac{dp}{dt}$

here k is the proportionality constant whose value is 1.

$f=\frac{dp}{dt}$

$f= \frac{d[mv]}{dt}$

$f= m\frac{dv}{dt} +v\frac{dm}{dt}$

$f=ma+v\frac{dm}{dt}$ [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.

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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 bottl...