A fleck moving horizontally to the right at 2.5 m/s begins to accelerate downward at 0.75 m/s2 . Where is the fleck 4.0 s later?
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To find the position of the fleck 4.0 s later, we can use the kinematic equations of motion.
First, let's determine the initial velocity of the fleck in the horizontal direction. Since it is moving horizontally to the right at a constant velocity of 2.5 m/s, the initial velocity in the horizontal direction (Vx) is 2.5 m/s.
Next, let's determine the initial velocity of the fleck in the vertical direction. Since the fleck is accelerating downward at 0.75 m/s^2, the initial velocity in the vertical direction (Vy) is 0 m/s (assuming the fleck starts from rest in the vertical direction).
Now, let's determine the vertical displacement (Δy) of the fleck after 4.0 s. We can use the equation:
Δy = Vy * t + 1/2 * a * t^2
where Δy is the vertical displacement, Vy is the initial vertical velocity, a is the acceleration in the vertical direction, and t is the time.
Plugging in the values, we have:
Δy = 0 * 4.0 + 1/2 * (-9.8) * (4.0)^2
Since the acceleration due to gravity is approximately -9.8 m/s^2 (negative because it's downward), we can simplify the expression to:
Δy = -1/2 * 9.8 * 16
Δy = -78.4 m
Since the displacement is negative, this indicates that the fleck has moved downward. Therefore, the fleck is 78.4 m below its initial position after 4.0 s.
Now, let's determine the horizontal displacement (Δx) of the fleck after 4.0 s. We can use the equation:
Δx = Vx * t
where Δx is the horizontal displacement, Vx is the initial horizontal velocity, and t is the time.
Plugging in the values, we have:
Δx = 2.5 * 4.0
Δx = 10 m
Therefore, the fleck is 10 m to the right of its initial position after 4.0 s.
In summary, after 4.0 s, the fleck is both 78.4 m below and 10 m to the right of its initial position.