A flower pot is thrown out of a window with a horizontal velocity of 8 m/s. If the window is 1.5 m off the ground, how far from the window does it land?
(horizontal velocity) x (time to fall)
The time to fall is
t = sqrt(2H/g)
H = 1.5 m
To find out how far from the window the flower pot lands, we need to analyze the motion in the vertical direction.
Let's assume that the flower pot lands on the ground after a time t. We can use the equation of motion to determine the time it takes for the flower pot to reach the ground:
h = u*t + (1/2)*g*t^2
Where:
h is the initial height of the flower pot (1.5 m)
u is the initial vertical velocity of the flower pot (0 m/s, as it was thrown horizontally)
g is the acceleration due to gravity (-9.8 m/s^2, since it acts downwards)
t is the time taken for the flower pot to reach the ground.
Rearranging the equation, we get:
(1/2)*g*t^2 + u*t - h = 0
Substituting the given values:
(1/2)*(-9.8)*t^2 + 0*t - 1.5 = 0
Simplifying the equation:
-4.9t^2 - 1.5 = 0
To solve this quadratic equation, we can use the quadratic formula:
t = (-b ± √(b^2 - 4ac))/(2a)
where a = -4.9, b = 0, and c = -1.5.
Substituting the values into the quadratic formula, we get:
t = (-0 ± √(0^2 - 4*(-4.9)*(-1.5)))/(2*(-4.9))
Simplifying the equation:
t = ± √(0 - 4*(-4.9)*(-1.5))/(-9.8)
t = ± √(0 - 29.4)/(-9.8)
t = ± √(29.4)/(-9.8)
Taking the positive value:
t = √(29.4)/(-9.8)
Calculating the value of t:
t ≈ 1.03 seconds
Now that we know the time it takes for the flower pot to reach the ground, we can calculate the horizontal distance traveled by the flower pot using the horizontal velocity:
Distance = Velocity * Time
Distance = 8 m/s * 1.03 s
Distance ≈ 8.24 meters
Therefore, the flower pot lands approximately 8.24 meters horizontally from the window.