Question

A ball is projected vertically upward .it's speed at half of max height is 20 m/s .the max height attained by it take g=10 ms
a) 35 m
b)15 m
c) 25 m
d) 40 m​

Answer 1

$\bf{\underline{\underline{Question}}}$

$\:$

A ball is projected vertically upward .it's speed at half of max height is 20 m/s .the max height attained by it take g=10 ms

a) 35 m

b)15 m

c) 25 m

d) 40 m

$\:$

$\bf{\underline{\underline{Given\:,}}}$

$\:$

$\small\tt{s\:=\:{\frac{h_{max}}{2}}\:\:\:\:,\:\:\:V\:=\:20}$

$\:$

$\bf{\underline{\underline{solution\:}}}$

$\:$

$\small\tt{at\:maximum\:height,}\\\\\\{\small\tt{\:v\:=\:0\:\:,\:u\:=\:\sqrt{2gh_{max}}}}$

$\:$

$\small\tt{Now\:using\:}$

$\:$

$\small\tt\blue{\underline{\boxed{v^{2}-u^{2}\:=\:2as}}}$

$\:$

$\small\tt{putting\:Respective\:values}$

$\:$

$\small\tt{20^{2}-(\sqrt{2gh_{max})^{2}}}\:=\: -2g{\frac{(h_{max})}{2}}$

$\:$

$\small\tt{400}\:=\:gh_{max}$

$\:$

$\small\tt{when\:\:\:\:g\:=\:10\:,}$

$\:$

$\small\tt{400}\:=\:(10)h_{max}$

$\:$

$\small\tt{\cancel\frac{400}{10}}\:=\:h_{max}$

$\:$

$\small\tt\blue{\underline{\boxed{40}}}\:=\:h_{max}$

$\:$

$\bf{\underline{\underline{Hope\:It\: Help\:You}}}$

Answer 2

Answer:

Given -

• The speed of the ball at half of its total height = 20 m/s.
• The ball is projected vertically upward.
• g = 10 m/s²

To Find -

• Maximum height attained by the ball ?

Solution -

Let us assume the maximum height attained by the ball as h m.

The ball will go h metres vertically and then will stop. Then instantly, it would start falling downwards again.

Let us use Newton's Equation to solve this.

First case : For Half Distance travelled by the ball.

➸ v² - u² = 2gs

➸ (20)² - (u)² = 2*(-10)*(h/2)

➸ 400² = -20*h/2* + u²

➸ 400 = -10h + u²

➸ u² = 400 + 10h .....(1)

Second case : For whole Distance travelled by the ball.

➸ v² - u² = 2gs

➸ (0)² - (u)² = 2*(-10)*(h)

➸ 0 = -20*h* + u²

➸ 0 = -20h + u²

➸ u² = 20h .....(2)

Now, equating both the equations.

➸ u² = 400 + 10h = 20h

➸ 400 = 10h

➸ h = 40 m

Hence, the maximum height attained by the ball thrown vertically upwards is D) 40 m.