The sears tower is nearly 400 m high. how long would it take a steel ball to reach the ground if dropped on the top? what will be it's velocity the moment for it touches the ground?

Answers:

a) 9.035 s

b) -88.543 m/s

Explanation:

The described situation is related to vertical motion (especifically free fall) and the equations that will be useful are:

(1)  

(2)  

Where:  

is the final height of the steel ball

is the initial height of the steel ball

is the initial velocity of the steel ball (it was dropped)

is the final velocity of the steel ball

is the time it takes to the steel ball to reach the ground

is the acceleration due to gravity

Knowing this, let's begin with the answers:

We will use equation (1) with the conditions listed above:

(3)  

Isolating :

(4)  

(5)  

(6)  

We will use equation (2) with the conditions explained above and the calculaated time:

(7)  

(8)  

(9)  The negative sign indicates the direction of the velocity is downwards

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