Tom the cat is chasing Jerry the mouse across
a table surface 1.8 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
7.6 m/s.
Where will Tom strike the floor? The acceleration of gravity is 9.8 m/s
2
.
Answer in units of m
Ha! I remember that episode. tom exploed
To solve this problem, we need to find the horizontal distance Tom will travel before striking the floor. Here's how you can calculate it:
1. Determine the time it takes for Tom to hit the floor. We can use the equation for vertical displacement:
Δy = vi * t + (1/2) * a * t^2
In this case, the initial velocity (vi) is 0 m/s since Tom is sliding off the edge of the table. The vertical displacement (Δy) is the height of the table, which is 1.8 m. The acceleration (a) is due to gravity and is -9.8 m/s^2 (negative because it acts in the opposite direction). Solving for time (t), we get:
1.8 m = 0.5 * (-9.8 m/s^2) * t^2
t^2 = (1.8 m) / (0.5 * (-9.8 m/s^2))
t^2 = -0.36734694 s^2
t ≈ 0.6060904 s
The time is positive because we only consider the positive root of the equation.
2. Now, we can find the horizontal distance (x) Tom will travel using his horizontal velocity (vx) and the time we just calculated:
x = vx * t
x = 7.6 m/s * 0.6060904 s
x ≈ 4.6153856 m
Therefore, Tom will hit the floor approximately 4.6154 meters away from the edge of the table.