Tom the cat is chasing Jerry the mouse across
a table surface 1.9 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
4.6 m/s.
Where will Tom strike the floor? The ac-
celeration of gravity is 9.8 m/s2 .
Answer in units of m
To determine where Tom will strike the floor, we need to find the horizontal distance he will travel before hitting the ground. We can use the horizontal motion equation:
d = v₀t + (1/2)a(t^2)
where:
d is the horizontal distance,
v₀ is the initial horizontal velocity (in this case, 4.6 m/s),
t is the time of flight, and
a is the horizontal acceleration, which in this case is 0 since there is no external force affecting Tom's horizontal motion.
First, we need to find the time of flight. To do this, we need to find the time it takes for Tom to hit the ground. We can use the vertical motion equation:
h = v₀t + (1/2)gt^2
where:
h is the height (1.9 m),
v₀ is the initial vertical velocity (0 m/s since Tom is sliding horizontally),
g is the acceleration due to gravity (-9.8 m/s²), and
t is the time of flight that we want to find.
Rearranging the equation, we have:
0 = -4.9t^2 + 1.9
Solving this quadratic equation will give us the time of flight.
-4.9t^2 + 1.9 = 0
t^2 = 1.9/4.9
t ≈ √(0.3878)
t ≈ 0.6221 s
Now that we have the time of flight, we can find the horizontal distance:
d = (4.6 m/s)(0.6221 s)
d ≈ 2.8586 m
Therefore, Tom will strike the floor approximately 2.8586 meters from the edge of the table.
Calculate how long (T) that it takes Tom to hit the ground. This depends only upon the height (H) and g, since the cat takes off horizontally.
(1/2) g T^2 = H
T = sqrt(2H/g)
Then multiply T by the horizontal velocity component of Tom, which remains constant at 4.6 m/s.
Sq[2*1.9/9.8]=.62
then,4.6*.62=2.9
2.9 m is your answer.