You throw a ball downward with an initial speed of 10 feet per second out of a window to the ground 20 feet below. How long will it take to hit the ground
You throw a ball downward with an initial speed of 10 feet per second out of a window to the ground 20 feet below. How long will it take to hit the ground
Well, this is a simple free-fall problem. We have an initial speed and a vertical distance, so, we use our traditional kinematic formulas to solve the problem:
First, we record what we have:
$\displaystyle \text{Initial Position: 0m}$
$\displaystyle \text{Final Position: 20m}$
$\displaystyle \text{Initial Velocity: }10\frac{ft}{sec}$
$\displaystyle \text{Final Velocity: ?}$
$\displaystyle \text{Time: ?}$
$\displaystyle \text{Acceleration: }32\frac{ft}{sec^2}$
Now, if there are 2 or less question marks, we can solve the problem, so it looks solvable.
The next part would be to pick the correct equation, A first step would be to find the final velocity, this equation is perfect for that:
$\displaystyle v_{fy}^2 = v_{iy}^2 + 2a(y_f - y_i)$
Now we plug in what we know:
$\displaystyle v_{fy}^2 = 100 + 64(20)$
$\displaystyle v_{fy} = \sqrt{1380}$
$\displaystyle v_{fy} = 37.15 \frac{ft}{sec}$
Now, we use what we have now to find the time, this equation is simple and elegant:
$\displaystyle v_{fy} = v_{iy} + a_yt$
$\displaystyle 37.15 = 10 + 32t$
$\displaystyle 27.15 = 32t$
$\displaystyle 0.85 sec = t$
And there you go.