When a stone is thrown horizontally, its initial vertical velocity is zero, and it only has an initial horizontal velocity. Assuming no air resistance, the horizontal velocity remains constant throughout the motion. Therefore, the horizontal component of the stone's velocity will remain at 15 m/s throughout the 4-second time interval.
So, after 4 seconds, the horizontal velocity of the stone will still be 15 m/s. However, we need to determine the vertical velocity at this time.
Since the stone is subject to the acceleration due to gravity (9.8 m/s²) in the vertical direction, its vertical velocity will increase by 9.8 m/s every second. After 4 seconds, the change in vertical velocity will be:
ΔV = g × t = 9.8 m/s² × 4 s = 39.2 m/s
The stone's initial vertical velocity is zero, so after 4 seconds, the stone will have a vertical velocity of 39.2 m/s downward.
To find the resultant velocity (magnitude and direction), we can use the Pythagorean theorem:
v = √(v_horizontal² + v_vertical²)
where v_horizontal is the horizontal velocity (15 m/s) and v_vertical is the vertical velocity (-39.2 m/s).
v = √(15² + (-39.2)²) v ≈ 42.6 m/s
The negative sign in the vertical velocity indicates that the stone is moving downward. Therefore, the velocity of the stone after 4 seconds is approximately 42.6 m/s downward with a horizontal velocity of 15 m/s.