a ball is thrown into the air with an initial velocity of 30m\s and a horizontal velocity of 10m\s. What's it's speed after 4 seconds?
The horizontal velocity remains unchanged, but the vertical changes.
In the vertical
vf=30-9.8t
find the vertical velocity, add it to the horizontal as VECTORS.
.....huh? that would make the vertical velocity negative
of course: negative means downward.
To determine the speed of the ball after 4 seconds, we need to break down the motion into its vertical and horizontal components.
First, let's consider the vertical motion. The initial velocity in the vertical direction is given as 30 m/s. As the ball is thrown vertically, the only force acting on it is gravity, causing it to decelerate at a rate of 9.8 m/s^2 downwards. Assuming no air resistance, we can use the equation of motion:
v = u + at
Where:
v = final vertical velocity
u = initial vertical velocity
a = acceleration
t = time
Plugging in the values, we have:
v = 30 m/s - 9.8 m/s^2 * 4 s
v = 30 m/s - 39.2 m/s
v = -9.2 m/s
Note that the negative sign indicates that the ball is moving in the opposite direction to its initial velocity. In other words, the ball is now moving downward.
Next, let's consider the horizontal motion. The initial horizontal velocity is given as 10 m/s. Since there are no horizontal forces acting on the ball, its horizontal velocity remains constant. Therefore, the horizontal speed after 4 seconds will still be 10 m/s.
To find the overall speed of the ball after 4 seconds, we'll use the Pythagorean theorem:
Speed = √(vertical speed^2 + horizontal speed^2)
Speed = √((-9.2 m/s)^2 + (10 m/s)^2)
Speed = √(84.64 + 100)
Speed = √184.64
Speed ≈ 13.59 m/s
Therefore, the speed of the ball after 4 seconds is approximately 13.59 m/s.