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A marble dropped from a bridge strikes the water in 5.0 s. what is the height of the bridge? (Answer in meters)A

1 Answer

Jun 6, 2018

$122.5 m$ $"122.5 m"$

Explanation:

Use equation of motion

$S = ut + \frac{1}{2} {at}^{2}$ $"S" = "ut" + 1/2"at"^2$

Where

$S =$ $"S ="$ Displacement covered
$u =$ $"u ="$ Initial velocity
$a =$ $"a ="$ Acceleration (It’s ${9.8 m/s}^{2}$ $"9.8 m/s"^2$ due to Earths gravity)
$t =$ $"t ="$ Time taken to cover displacement $S$ $"S"$

Marble is dropped. It means initial velocity ( $u$ $"u"$ ) of marble is $0$ $0$

Therefore the equation becomes

$S = \frac{1}{2} {at}^{2}$ $"S" = 1/2"at"^2$

$S = \frac{1}{2} \times {9.8 m/s}^{2} \times {(5 s)}^{2}$ $color(white)("S") = 1/2 × "9.8 m/s"^2 × "(5 s)"^2$

$color(white)("S") = 122.5\ "m"$

Displacement covered by the marble when thrown from the bridge is obviously height of the bridge.

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