Tom the cat is chasing Jerry the mouse across the surface of a table 1.4 m above 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 5.8 m/s. Where will Tom strike the floor?
1) figure how long to fall 1.4m
h=1/2 g t^2
2) how far horizontally does the object go in time t? distance=t/5.8
To find where Tom will strike the floor, we need to determine how far Tom will travel horizontally before hitting the ground. The vertical distance that Tom falls does not affect the horizontal distance he travels.
We can use the equation of motion:
s = ut + (1/2)at^2
In this case, since Tom is sliding off the edge of the table horizontally, his initial vertical velocity (u) is 0 m/s, and the vertical acceleration (a) due to gravity is approximately 9.8 m/s^2 (assuming no air resistance).
We know the time it takes for Tom to hit the ground is the same as the time it takes for an object to fall from a height of 1.4 m, so we can use the equation:
s = ut + (1/2)at^2
Rearranging the equation, we have:
t = sqrt((2s)/a)
Substituting the values, we have:
t = sqrt((2 * 1.4) / 9.8)
t = sqrt(0.28 / 9.8)
t = sqrt(0.0286)
t ≈ 0.169 s
Now, we can use the equation of motion for horizontal motion:
s = ut
Since Tom's initial horizontal velocity (u) is 5.8 m/s, and the time (t) is 0.169 s, we can calculate the horizontal distance (s) traveled by Tom before hitting the ground:
s = ut
s ≈ 5.8 * 0.169
s ≈ 0.9792 m
Therefore, Tom will strike the floor approximately 0.9792 meters away from the edge of the table.