Question

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?

Answer 1

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

$v_i = v_ocos\theta \hat i + v_o sin\theta\hat j$

now its acceleration due to gravity is given as

$a = 0 - g\hat j$

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

$v_f = v_i + at$

$v_f = v_ocos\theta \hat i + (v_o sin\theta - gt)\hat j$

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

$v_f = v_o cos\theta \hat i$

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.

Answer 2

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 !!