Find the horizontal and vertical components of the velocity of a cannonball 4 seconds after being fired horizontally at 400 m/s from the edge of a tall cliff.
vertical: -g*t=-4g
horizontal: 400, neglecting air resistance.
To find the horizontal and vertical components of the velocity of the cannonball, we need to consider the motion of the cannonball separately in the horizontal and vertical directions.
Given:
Initial velocity (v₀) = 400 m/s
Time (t) = 4 s
Horizontal component of velocity (Vx):
The horizontal component of the velocity remains constant throughout the motion because the cannonball is fired horizontally. Therefore, the horizontal component of the velocity is equal to the initial horizontal velocity.
Vx = v₀ = 400 m/s
Vertical component of velocity (Vy):
The vertical component of the velocity changes due to the influence of gravity. The vertical motion of the cannonball can be described by the equation of motion:
Vy = v₀ + (g * t)
where g is the acceleration due to gravity, which is approximately 9.8 m/s².
Vy = 400 m/s + (9.8 m/s² * 4 s)
Vy = 400 m/s + 39.2 m/s
Vy = 439.2 m/s
Therefore, the horizontal component of the velocity is 400 m/s, and the vertical component of the velocity is approximately 439.2 m/s.
To find the horizontal and vertical components of the velocity of the cannonball, we can make use of the fact that horizontal and vertical motions are independent of each other.
Given:
Initial velocity (v₀) = 400 m/s (horizontal)
Time (t) = 4 seconds
Horizontal Component of Velocity (Vx):
Since the cannonball was fired horizontally, its horizontal component of velocity remains constant throughout its motion. Therefore, the horizontal component of velocity (Vx) at any point in time will be equal to the initial horizontal velocity (v₀).
Vx = v₀ = 400 m/s
Vertical Component of Velocity (Vy):
To find the vertical component of velocity (Vy) at a specific time, we need to consider the effect of gravity on the cannonball.
The acceleration due to gravity (g) acts only in the vertical direction, causing the object to accelerate downwards. The equation to calculate the vertical component of velocity (Vy) at a given time (t) is:
Vy = v₀ + g * t
Where:
v₀ = initial vertical velocity (which is zero in this case as the cannonball was fired horizontally)
g = acceleration due to gravity (typically taken as 9.8 m/s²)
t = time
Plugging in the known values, we have:
Vy = 0 + (9.8 m/s²) * 4 s
= 0 + 39.2 m/s
= 39.2 m/s
Therefore, the horizontal component of velocity (Vx) remains 400 m/s, while the vertical component of velocity (Vy) is 39.2 m/s.