You throw a ball downward from a window at a speed of 1.8 m/s. How fast will it be moving when it hits the sidewalk 2.8 m below?
I will be happy to critique your thinking on this.
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To determine how fast the ball will be moving when it hits the sidewalk, we can use the equation of motion for an object in free fall.
In this case, the initial velocity of the ball is 1.8 m/s (thrown downwards), the acceleration is due to gravity, which is approximately 9.8 m/s^2 (assuming no air resistance), and the displacement is 2.8 m (the distance below the window).
We can use the following equation of motion to solve for the final velocity:
v^2 = u^2 + 2as
where:
v = final velocity
u = initial velocity
a = acceleration
s = displacement
Plugging in the given values, we get:
v^2 = (1.8 m/s)^2 + 2 * 9.8 m/s^2 * 2.8 m
v^2 = 3.24 m^2/s^2 + 54.88 m^2/s^2
v^2 = 58.12 m^2/s^2
To find the final velocity, we take the square root of both sides:
v = √(58.12 m^2/s^2)
v ≈ 7.63 m/s
Therefore, the ball will be moving at a speed of approximately 7.63 m/s when it hits the sidewalk 2.8 m below.