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jekas [21]
3 years ago
14

A(n) 0.576 kg soccer ball approaches a player horizontally with a speed of 20.9 m/s. The player illegally strikes the ball with

her hand and causes it to move in the opposite direction with a speed of 9.73 m/s. What is the magnitude of the impulse delivered to the ball by the player?
Physics
1 answer:
Travka [436]3 years ago
4 0

Answer:

17.6kg.m/s in the opposite direction of the initial velocity.

Explanation:

In order to solve this we can use the Impulse-Momentum theorem:

J=\Delta p\\J=m(v_f-v_o)

We will assume the motion of the ball approaching the player as positive, so:

J=0.576kg((-9.73m/s)-20.9m/s)=-17.6kg.m/s

So the impulse is 17.6kg.m/s in the opposite direction of the initial velocity.

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2. A 20 cm object is placed 10cm in front of a convex lens of focal length 5cm. Calculate
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<u> </u><u>»</u><u> </u><u>Image</u><u> </u><u>distance</u><u> </u><u>:</u>

{ \tt{ \frac{1}{v}  +  \frac{1}{u} =  \frac{1}{f}  }} \\

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{ \tt{ \frac{1}{v} +  \frac{1}{10} =  \frac{1}{5}   }} \\  \\  { \tt{ \frac{1}{v}  =  \frac{1}{10} }} \\  \\ { \tt{v = 10}} \\  \\ { \underline{ \underline{ \pmb{ \red{ \: image \: distance \: is \: 10 \: cm \:  \: }}}}}

<u> </u><u>»</u><u> </u><u>Magnification</u><u> </u><u>:</u>

• Let's derive this formula from the lens formula:

{ \tt{ \frac{1}{v}  +  \frac{1}{u} =  \frac{1}{f}  }} \\

» Multiply throughout by fv

{ \tt{fv( \frac{1}{v} +  \frac{1}{u} ) = fv( \frac{1}{f}  )}} \\   \\ { \tt{ \frac{fv}{v}  +  \frac{fv}{u}  =  \frac{fv}{f} }} \\  \\  { \tt{f + f( \frac{v}{u} ) = v}}

• But we know that, v/u is M

{ \tt{f + fM = v}} \\  { \tt{f(1 +M) = v }} \\ { \tt{1 +M =  \frac{v}{f}  }} \\  \\ { \boxed{ \mathfrak{formular :  } \: { \tt{ M =  \frac{v}{f}  - 1 }}}}

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{ \tt{M =  \frac{10}{5} - 1 }} \\  \\ { \tt{M = 5 - 1}} \\  \\ { \underline{ \underline{ \pmb{ \red{ \: magnification \: is \: 4}}}}}

<u> </u><u>»</u><u> </u><u>Nature</u><u> </u><u>of</u><u> </u><u>Image</u><u> </u><u>:</u>

  • Image is magnified
  • Image is erect or upright
  • Image is inverted
  • Image distance is identical to object distance.
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