Aball is thrown an intial velocity of (6i+7j).when it reaches to the rop of trajectory.(neglegating air resistance). what its velocity

Velocity = 6 units per unit time

Explanation:

Given:

Initial velocity of the ball is,

The velocity is given in vector form. The component along the x direction is the horizontal component and the component along the y direction is the vertical component of initial velocity.

Therefore, the horizontal component = 6 units per unit time.

Vertical component = 7 units per unit time

The motion of the ball is a projectile motion with initial velocity at some angle to the horizontal.

The motion of a projectile can be split into horizontal and vertical motions. Along the vertical direction, the force acting on the ball is due to gravity and thus the velocity in that direction goes on decreasing as the acceleration acts in the downward direction.

At the top of the trajectory, the vertical component of velocity becomes zero as that is the maximum vertical height of the projectile.

Only horizontal component of velocity acts at the highest point. The horizontal component of velocity doesn't change with time as there is no force acting in the horizontal direction to increase or decrease the speed in that direction.

So, at the highest point, the horizontal component of velocity is equal to the  horizontal component of initial velocity and is equal to 7 units per unit time.

The vertical component is zero. Hence, the velocity at the highest point is equal to horizontal component only and is equal to 7 units per unit time.