Physics, asked by komaljain38, 10 months ago

for an object thrown 45° to horizontal the maximum height H and horizontal range R are releated as​

Answers

Answered by nirman95
6

Answer:

Given:

Object thrown (projected) at 45°

To find:

Relationship between H and R

Calculation:

For 45° angle of Projection, we get max value of Range (R) ;

R =  \dfrac{ {u}^{2} \sin(2 \theta)  }{g}

Putting available values :

 =  > R =  \dfrac{ {u}^{2} \sin(2  \times 45 \degree)  }{g}

 =  > R =  \dfrac{ {u}^{2} \sin( 90 \degree)  }{g}

 =  > R =  \dfrac{ {u}^{2}   }{g} .....(1)

Coming to max Height :

H =  \dfrac{ {u}^{2}  { \sin}^{2} (\theta) }{2g}

Putting available values:

 =  > H =  \dfrac{ {u}^{2}  { \sin}^{2} (45 \degree) }{2g}

 =  > H =  \dfrac{ {u}^{2}   { (\frac{1}{ \sqrt{2} } )}^{2}  }{2g}

 =  > H =  \dfrac{1}{4}  \times   \bigg(\dfrac{ {u}^{2} }{g}  \bigg)

 =  > H =  \dfrac{R}{4}

So relationship is as follows:

 \boxed{ \red{ \huge{ \bold{H =  \dfrac{R}{4} }}}}

Answered by Anonymous
10

Solution :

Given:

✏ Angle of projection = 45°

To Find:

✏ Relation between maximum height (H) and horizontal range (R)

Formula:

  • Maximum height

 \star \:  \boxed{ \bold{ \tt{ \pink{H =  \dfrac{ {u}^{2} { \sin}^{2}  \theta }{2g}}}}}  \:  \star

  • Horizontal range

 \star \:  \boxed{ \bold{ \green{ \tt{R =  \dfrac{ {u}^{2}  \sin2 \theta}{g}}}}}  \:  \star

Calculation:

__________________________________

  • Maximum height

 \dashrightarrow \sf \: H =  \dfrac{ {u}^{2}  { \sin}^{2} 45 \degree }{2g}  \\  \\  \dashrightarrow \sf \:  \red{H =  \dfrac{ {u}^{2} }{4g}  }

__________________________________

  • Horizontal range

 \rightarrowtail \sf \: R =  \dfrac{ {u}^{2}  \sin2(45 \degree)}{g}  \\  \\  \rightarrowtail \sf \: R =  \dfrac{ {u}^{2} \sin90 \degree }{g}  \\  \\  \rightarrowtail \sf \:  \blue{R =  \dfrac{ {u}^{2} }{g} }

__________________________________

 \mapsto \sf \:  \dfrac{R}{H}  =  \dfrac{ {u}^{2}}{g} \times  \dfrac{4g}{ {u}^{2} }  \\  \\  \mapsto \sf \:  \frac{R}{H}  = 4 \\  \\  \mapsto \:  \boxed{ \tt{  \huge{\orange{R = 4H}}}}

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