Question

a grasshopper can jump into a height h. find the maximum distance through with it can along the horizontal ground ​

Answer 1

Answer:

The grasshopper can jump upto a height h. It means the maximum possible height it can achieve,

i.e., when it jumps vertically.

Now, maximum range,

v2g=2ghg

=2h

⇒R=2h.

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Answer 2

Given,

A grasshopper can jump into a height h. That is, it can attain its highest height when it jumps vertically (along the y-axis).

To find -

Te maximum distance through with it can along the horizontal ground.

Solution ↓

$\sf{h=\dfrac{v^2sin^2\theta}{2g} }$

Where θ = 90°

$\sf{\hookrightarrow h=\dfrac{v^2}{2g} }\\\\\sf{\hookrightarrow v^2= 2gh}$

Now, we know :-

$\sf{R_{max}=\dfrac{v^2}{g} }\\\\\sf{\hookrightarrow R_{max}=\dfrac{2gh}{g} }\\\\\boxed{\sf{\hookrightarrow R_{max}=2h}}$

Hence, the maximum distance through with it can along the horizontal ground ​ is 2h.