An arrow is straight up into the air. When it reaches its highest point in the air,
When an arrow is shot straight up in the air, there are two factors which oppose the motion of the arrow. It is because of these factors that the arrow does not continue travel infinitely and ultimately comes to a halt and then returns. These two factors are earth's gravitational force and air resistance.
Of these two factors, air resistance is negligible considering the streamlined shape of an arrow, and hence we can safely ignore its effect. The major factor is then the earth's gravitational force.
To calculate the highest point, we will use the equations of motion.
If the initial velocity of the arrow is , the arrow will continue to travel upwards until its velocity becomes zero. So, final velocity of the arrow . Let the time taken by the arrow to reach the highest point be . To find we will use the equation of motion,
where is the acceleration.
For the arrow, the acceleration is due to earth's gravitational force and it directed downwards. So our equation becomes,
where g is acceleration due to gravity and the minus sign is due to the fact that is acting in the direction opposite to the direction of its motion. So, putting ,
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