A stone of mass m is thrown upward at a 30? angle to the horizontal. At the instant the stone reaches its highest point, why is the stone neither gaining nor losing speed?

First you need to know to gain or lose speed you must have acceleration of deacceleration in the direction of speed !!

so at highest point , the only acceleration is gravity and that is in the downward direction so , the velocity remains constant !!

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aristocles aristocles · Answer 2 · 2019-04-22T02:09:59+02:00

Answer:

At highest point of the path the acceleration is perpendicular to velocity direction so there is no change in speed at this moment.

Explanation:

When an object is thrown at an angle of 30 degree with the horizontal with some initial speed

then we will have

[tex]v_i = v_ocos\theta \hat i + v_o sin\theta\hat j[/tex]

now its acceleration due to gravity is given as

[tex]a = 0 - g\hat j[/tex]

with the help of kinematics we can say that its velocity after any time "t" is given as

[tex]v_f = v_i + at[/tex]

[tex]v_f = v_ocos\theta \hat i + (v_o sin\theta - gt)\hat j[/tex]

now when it will reach to its highest point then its velocity in y direction becomes zero

[tex]v_f = v_o cos\theta \hat i[/tex]

now since final velocity is along x direction only at the highest point while its acceleration at that point is due to gravity so at that moment there is no change in speed.