I have no idea how to do this! please help me! (there are 5 Parts) Please show w

Question

I have no idea how to do this! please help me! (there are 5 Parts)
Please show work so I can learn how to solve it! thanks!! :)

1. Galileo's great-great-great grandchild stands at the top of a vertical tower 59.4 m tall with a Chianti bottle.
How long does it take for the bottle to fall to the ground, if it was just dropped from the tower?


2. What is the velocity of the bottle as it hits the ground, if it was just dropped from the tower?


3. How far does the bottle land from a point on the ground directly beneath the point from which it was launched, if the bottle was thrown straight out horizontally from the tower with a speed of 12.3 m/s?

4. What is the bottle's horizontal component of velocity, if the bottle was thrown straight out horizontally from the tower with a speed of 12.3 m/s?


5. What is the magnitude of its velocity just before it strikes the ground, if the bottle was thrown straight out horizontally from the tower with a speed of 12.3 m/s?

Explanation / Answer

(1). height h = 59.4 m required time t = [ 2h / g ]      Since h = ut + ( 1/ 2) gt^ 2   where u = 0                         = 3.481 s (2). required velocity v = [ 2gh ]   Since v^ 2- u^ 2 = 2gh     where u = 0                                     = 34.12 m / s (3). horizontal speed u = 12.3 m / s required distance = range                            = horizontal component of velocity * time of flight                              = u * [ 2h / g ]                              = 42.81 m (4).  the bottle's horizontal component of velocity = 12.3 m / s since there is no acclerationn along horizontal .So, horizontal velocity is not changed (5). the magnitude of its velocity just before it strikes the ground V = [ u^ 2 + (gt)^ 2]               V = 36.26 m / s

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