A young girl standing on a bridge throws a stone with an initial downward veloci

Question

A young girl standing on a bridge throws a stone with an initial downward velocity at an angle of 45 degrees in an attempt to hit a block of wood floating in the river below.

a. If the stone is thrown from a height of 20m and it takes 1.73s to reach the water, what is the initial component of the y velocity?

b. Using the y-component of the velocity and the angle, determine the initial speed (the magnitude of overall initial velocity)

c. Use the x-component of the velocity and the time to determine whether or not the stone will hit a block of wood that is 5 meters away from the bridge and is 0.5m in length.

Explanation / Answer

Angle = 45 degrees Height h = 20 m Time taken to reach the water t = 1.73 s Let the initial component of the y velocity u = ? From the relation h = ut + ( 1/ 2) gt 2                         20 = 1.73 u + 14.66                           u = 3.083 m / s (b). we know u = v sin Initial speed of the stone v = u / sin                                              = 4.36 m / s (c). x-component of velocity V = v cos                                                = 3.083 m / s Time of flight T = 1.73 s Range R = VT               = 5.33 m Distance of the wood from bridge S = 5m Length of the wood L = 0.5m S <R < (S+L) The stone hits the wood

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