A cat, walking along the window ledge of a New York apartment, knocks off a flower pot, which falls to the street 210 feet below. How fast is the flower pot traveling when it hits the street? (Give your answer in ft/s and in mi/hr, given that the acceleration due to gravity is 32 ft/s^2 and 1 ft/s = 15/22 mi/hr.)
Well, that's quite the curious cat! Let's calculate the speed of the flower pot when it hits the street, shall we?
To find the speed, we can use the equation of motion: v^2 = u^2 + 2as. Here's how we can break it down:
Initial velocity (u) = 0 ft/s (since the flower pot was dropped)
Acceleration (a) = 32 ft/s^2 (as gravity pulls it down)
Displacement (s) = 210 ft (the height from the window ledge to the street)
Final velocity (v) = ???
Rearranging the equation, we have v^2 = 0^2 + 2(32)(210).
Simplifying that, v^2 = 0 + 13440.
Taking the square root of both sides, we get v ≈ √13440 ft/s.
But you also wanted the speed in mi/hr, so let's convert. Remember, 1 ft/s = 15/22 mi/hr.
Converting, we have v ≈ √13440 * (15/22) mi/hr.
Calculating that, v ≈ 601.55 * (15/22) mi/hr.
Finally, v ≈ 409.23 mi/hr (rounded to two decimal places).
So, when that flower pot reaches the street, it'll be zipping along at approximately 601.55 ft/s or 409.23 mi/hr (if my calculations are correct). Just be glad you're not walking below that window ledge!
To find the speed of the flower pot when it hits the street, we can use the kinematic equation:
v^2 = u^2 + 2as
Where:
v = final velocity (speed of the flower pot when it hits the street)
u = initial velocity (speed of the flower pot right before it falls, which is 0 ft/s since it was knocked off the window ledge)
a = acceleration (acceleration due to gravity, which is -32 ft/s^2 since it's acting downwards)
s = distance traveled (height of the window ledge, which is 210 ft)
Substituting the given values into the equation:
v^2 = 0^2 + 2(-32)(210)
Simplifying:
v^2 = 0 + (-6720)
v^2 = -6720
Since velocity cannot be negative in this case, we can ignore the negative sign:
v = √6720 ft/s
To convert this to mi/hr, we use the conversion factor: 1 ft/s = 15/22 mi/hr
v = √(6720)(15/22) mi/hr
Now let's calculate:
v ≈ √4500 ≈ 67.082
Therefore, the speed of the flower pot when it hits the street is approximately 67.082 ft/s or 67.082(15/22) ≈ 45.682 mi/hr.
To find the speed at which the flower pot hits the street, we can use the principle of conservation of energy. The potential energy lost by the flower pot as it falls equals the kinetic energy gained.
The potential energy lost by the flower pot is given by the formula:
Potential Energy = mass * gravity * height
We are given the acceleration due to gravity as 32 ft/s^2 and the height as 210 feet. To find the mass of the flower pot, we need additional information.
Once we know the mass, we can calculate the potential energy lost. Since potential energy is converted into kinetic energy as the flower pot falls, we can equate potential energy to kinetic energy:
Potential Energy = Kinetic Energy
The kinetic energy of an object is given by the formula:
Kinetic Energy = 0.5 * mass * velocity^2
By equating potential energy to kinetic energy, we obtain:
mass * gravity * height = 0.5 * mass * velocity^2
From this equation, we can solve for velocity:
velocity^2 = 2 * gravity * height
Taking the square root of both sides, we get:
velocity = √(2 * gravity * height)
Now we can substitute the values into the equation to find velocity in ft/s:
velocity = √(2 * 32 ft/s^2 * 210 ft)
Simplifying this equation will give us the final answer in ft/s.
To convert ft/s to mi/hr, we can use the conversion factor provided: 1 ft/s = 15/22 mi/hr. By multiplying the result obtained in ft/s by 15/22, we can calculate the speed in mi/hr.
you know that s = 1/2 at^2 and v = at, so v = √(2as)
v = √(2*32*210) ft/s
I expect you can convert that to mi/hr.