Question

A ball is thrown vertically upward. It has a speed of 10 m/s when it has reached one half of its maximum height. How high does the ball rise? (Taking g = 10 m/s2) [AIPMT (Prelims)-2005] (1) 15 m (2) 10 m (3) 20 m (4) 5 m
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Answer 1

Answer:

Given :-

• A ball is thrown vertically upward.
• It has a speed of 10 m/s when it has reached one half of its maximum height.

To Find :-

• What is the height does the ball rise.

Solution :-

Given :

• Final Velocity = 0 m/s
• Initial Velocity = 10 m/s
• Acceleration due to gravity = 10 m/s²

According to the question by using the formula we get,

$\implies \sf\bold{\pink{v^2 =\: u^2 - 2gh}}$

$\implies \sf (0)^2 =\: (10)^2 - 2 \times 10 \times \dfrac{h}{2}$

$\implies \sf (0 \times 0) =\: (10 \times 10) - 20 \times \dfrac{h}{2}$

$\implies \sf 0 =\: 100 - \dfrac{20h}{2}$

$\implies \sf 0 =\: 100 - 10h$

$\implies \sf 0 - 100 =\: - 10h$

$\implies \sf {\cancel{-}} 100 =\: {\cancel{-}} 10h$

$\implies \sf \dfrac{100}{10} =\: h$

$\implies \sf 10 =\: h$

$\implies \sf\bold{\red{h =\: 10\: m}}$

$\therefore$ The maximum height does the ball rise is 10 m .

Hence, the correct options is option no (2) 10 m .

Answer 2

Answer :

• 10m

Given :

• A ball is thrown vertically upward.It has a speed of 10 m/s when it has reached one half of its maximum height

To find :

• How high does the ball rise.

Solution :

Given :

• Final Velocity = 0 m/s
• Initial Velocity = 10 m/s
• Acceleration (gravity) = 10m/s²

According to question :

we know that

• v² = u² - 2gh

⇢ v² = u² - 2gh

⇢ (0)² = (10)² - 2 × 10 × h/2

⇢ 0 × 0 = 10 × 10 - 20 × h/2

⇢ 0 = 100 - 20h/2

⇢ 0 = 100 - 10h

⇢ 0 - 100 = -10h

⇢ -100 = -10h

⇢ 100/10 = h

⇢ h = 100/10

⇢ h = 10m

Hence , Answer is 10m.