If an object is thrown horizontally with an initial speed (velocity) of v, and then it is released, the object will experience vertical motion due to the force of gravity while its horizontal velocity remains constant.
In the absence of air resistance, the horizontal velocity of the object will not change over time. Therefore, after t seconds, the horizontal velocity of the object will still be v.
However, the object will experience a downward acceleration due to gravity (approximately 9.8 m/s² near the surface of the Earth). As a result, the object's vertical velocity will increase over time due to the acceleration.
The vertical velocity (Vy) at any given time t can be calculated using the equation:
Vy = gt
where g represents the acceleration due to gravity.
Since the object was thrown horizontally, there is no initial vertical velocity (Vy = 0) when it was released. Thus, after t seconds, the object's velocity can be represented as a vector:
Velocity = (v, gt)
Here, the horizontal velocity component remains v, and the vertical velocity component increases linearly with time, following the equation Vy = gt.
In summary, the object's velocity after t seconds can be represented as (v, gt), where v is the initial horizontal velocity and g is the acceleration due to gravity.