Tom the cat is chasing Jerry the mouse across
a table surface 2.4 m off the floor. Jerry steps
out of the way at the last second, and Tom
slides off the edge of the table at a speed of
4.8 m/s.
Where will Tom strike the floor? The acceleration of gravity is 9.8 m/s
2
h = 0.5g*t^2 = 2.4 m.
4.9t^2 = 2.4
t^2 = 0.490
Tf = 0.7 s.
Dx = Xo * Tf = 4.8m/s * 0.7s = 3.36 m from the table.
To determine where Tom will strike the floor, we need to calculate the horizontal distance he travels before falling.
First, let's find the time it takes for Tom to fall from the edge of the table to the floor. We can use the equation of motion:
d = v₀t + 0.5at²
In this case, the initial velocity v₀ is 4.8 m/s, the acceleration a is -9.8 m/s² (negative as it opposes the upward direction), and the distance d is 2.4 m. Plugging in these values, we can rearrange the equation to solve for t:
2.4 = 4.8t + 0.5(-9.8)t²
0.5(-9.8)t² + 4.8t - 2.4 = 0
Now, we can solve this quadratic equation for t using the quadratic formula:
t = (-b ± √(b² - 4ac)) / (2a)
In this case, a = 0.5(-9.8) = -4.9, b = 4.8, and c = -2.4. Plugging in these values:
t = (-4.8 ± √(4.8² - 4(-4.9)(-2.4))) / (2(-4.9))
Now, we can calculate t using a calculator. The two values obtained from the quadratic formula are the possible times it takes for Tom to fall to the ground. We will consider the positive value since time cannot be negative:
t ≈ 0.614 seconds
Now, we can calculate the horizontal distance Tom travels during this time. We use the equation:
d = v₀t
Here, the initial velocity v₀ is 4.8 m/s and the time t is 0.614 seconds:
d = 4.8 m/s * 0.614 s
d ≈ 2.9472 meters
Therefore, Tom will strike the floor approximately 2.9472 meters away from the edge of the table in the horizontal direction.