A hockey puck slides off the edge of a table with the initial velocity of 20m/s. The table height is 2.0 m. What is the accleration of the puck right after it leaves the table?
find how long it takes a puck to fall 2 m.
2=1/2 g t solve for t.
distance horizontal: 20*t
To find the acceleration of the puck right after it leaves the table, we need to use the kinematic equations.
First, let's calculate the time it takes for the puck to fall from the table to the ground. We can use the equation:
y = v0 * t + (1/2) * a * t^2
where
y = total vertical distance traveled (in this case, 2.0 m),
v0 = initial vertical velocity (in this case, 20 m/s),
a = acceleration (which we're trying to find),
t = time
Since the puck slides horizontally off the table, we can ignore any horizontal motion and focus only on the vertical motion. Therefore, the initial vertical velocity v0 is equal to 0 m/s.
Now, we can rewrite the equation as:
y = (1/2) * a * t^2
Plugging in the given values, we get:
2.0 = (1/2) * a * t^2
Next, since we want to find the time it takes for the puck to reach the ground, we can use the equation:
y = (1/2) * g * t^2
where g is the acceleration due to gravity, which is approximately 9.8 m/s^2 on Earth.
Substituting this value into the equation, we have:
2.0 = (1/2) * 9.8 * t^2
Now, we can solve for t:
2.0 = 4.9 * t^2
t^2 = 2.0 / 4.9
t ≈ 0.643 s
So, it takes approximately 0.643 seconds for the puck to fall from the table to the ground.
Now, to find the acceleration of the puck right after it leaves the table, we can use the equation:
v = v0 + a * t
where
v = final velocity (which is 0 m/s at the moment the puck leaves the table),
v0 = initial velocity (which is 20 m/s),
a = acceleration (which we're trying to solve for),
t = time (which we just found to be approximately 0.643 s)
Substituting the given values, we have:
0 = 20 + a * 0.643
Rearranging the equation to solve for a, we get:
a * 0.643 = -20
a ≈ -31.09 m/s^2
Therefore, the acceleration of the puck right after it leaves the table is approximately -31.09 m/s^2, directed downwards.