Question

To estimate the height of a bridge over a river ,a stone is dropped freely in the river from the bridge. the stone takes 2 seconds to touch the water surface in the river calculate the height of the bridge from the water level (g=9.8m/s²)

Answer 1

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

• To estimate the height of a bridge over a river, a stone is dropped freely in the river from the bridge. The stone takes 2 seconds to touch the water surface in the river calculate the height of the bridge from the water level (g = 9.8 m/s²)

$\red{\underline{{ \bf AnSwer }}}$

$\underline {\underline{{\purple{ \sf Given }}}}$

• Initial Velocity (u) = 0 m/s
• Time Taken (t) = 2 second
• Acceleration due to gravity (g) = 9.8 m/s²

$\underline {\underline{{ \purple{\sf To \: Find }}}}$

• Height (h)

$\underline {\underline{{ \green{\sf Calculating \: Height }}}}$

Formula Used :- $\underline{\underline{\boxed{ \pink{\sf h = ut + \dfrac{1}{2} gt^{2} }}}}$

Substituting Values

☞ h = 0 × 2 + ½ × 9.8 × (2)²

☞ h = 0 + ½ × 9.8 × 4

☞ h = 1 × 9.8 × 2

☞ h = 9.8 × 2

☞ h = 19.6

Therefore, the height of the bridge from the water level is 19.6 meters

$\red{\underline{{ \bf Important \: Formula }}}$

1. v = u + gt
2. h = ut + ½ gt²
3. v² - u² = 2gh

Answer 2

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Question :

• To estimate the height of a bridge over a river ,a stone is dropped freely in the river from the bridge. the stone takes 2 seconds to touch the water surface in the river calculate the height of the bridge from the water level (g=9.8 m/s²)

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Given:

• As the stone is dropped freely the initial velocity of the stone is 0 hence u = 0 m/s
• time taken by the stone to reach the water surface = 2 sec

• acceleration due to gravity= 9.8  m/s²

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To find :

• height of the bridge from the water level

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Solution :

By using the second kinematic equation ,

>> h= u t +1 x g t ² /2

here,

• h = height of the bridge from the water level

• u = initial velocity
• g = acceleration due to gravity
• t = time taken

Substituting the given values we get ,

-> h = g t ² /2

-> h = 9.8 x 4 / 2

-> h = 9.8 x 2

-> h = 19.6 m

The height of the bridge from the water level is 19.6 m

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Hope this helps :D