Two stones are launched from the top of a tall building. One stoneis thrown in a direction 30.0^\circ above the horizontal with aspeed of 16.0 \rm {m/s}; the other is thrown in adirection 30.0^\circ below the horizontal with thesame speed.
Part A
Which stone spends more time in the air?(Neglect air resistance.)
The stone thrown upward
Part B
Which stone lands farther away from the building? (Neglect air resistance.)
They would land in the same spot correct? just at different times...?

Part A)

t(1) > t(2), the stone thrown 30 above the horizontal spends more time in the air.

Part B)

x(f1) > x(f2), the first stone will land farther away from the building.

Explanation:

Part A)

Let's use the parabolic motion equation to solve it. Let's define the variables:

y(i) is the initial height, it is a constant.y(f) is the final height, in our case is 0v(i) is the initial velocity (v(i)=16 m/s)θ1 is the first angle, 30°θ2 is the first angle, -30°

For the first stone

             

(1)  

For the second stone  

   

(2)            

 

If we solve the equation (1) we will have:

 

We can do the same procedure for the equation (2)

We can analyze each solution to see which one spends more time in the air.

It is easy to see that the value inside the square root of each equation is always greater than 8, assuming that the height of the building is > 0. Now, to get positive values of t(1) and t(2) we need to take the negative option of the square root.

Therefore, t(1) > t(2), it means that the stone thrown 30 above the horizontal spends more time in the air.

Part B)

We can use the equation of the horizontal position here.

First stone

Second stone

Knowing that t(1) > t(2) then x(f1) > x(f2)

Therefore, the first stone will land farther away from the building.

They land at different points at different times.

I hope it helps you!

Is a  vector quantity  that refers to "the rate at which an object changes its position." imagine a person moving rapidly - one step forward and one step back - always returning to the original starting position. while this might result in a frenzy of activity, it would result in a zero velocity. because the person always returns to the original position, the motion would never result in a change in position. since velocity is defined as the rate at which the position changes, this motion results in zero velocity. if a person in motion wishes to maximize their velocity, then that person must make every effort to maximize the amount that they are displaced from their original position. every step must go into moving that person further from where he or she started. for certain, the person should never change directions and begin to return to the starting position.

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