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
And what speed will he have just before hitting the ground?
how long does it take to fall 2.4m?
4.9t^2 = 2.4
during that time, Tom will travel at 4.8 m/s horizontally.
The vertical component of the velocity is v=9.8t
Now just add the two components to get the resultant velocity.
To find where Tom will strike the floor and the speed he will have just before hitting the ground, we can use the equations of motion.
First, let's find the time it takes for Tom to hit the ground. We know that the vertical distance from the table surface to the floor is 2.4 m. The acceleration due to gravity is 9.8 m/s^2.
Using the equation:
d = ut + (1/2)at^2
where:
d = displacement (2.4 m)
u = initial velocity (0 m/s, as Tom slides off the edge)
a = acceleration due to gravity (-9.8 m/s^2)
t = time
Rearranging the equation, we get:
t^2 - 2.4 = (0.5)(-9.8)t^2
0.5(-9.8)t^2 - t^2 = -2.4
Simplifying further:
-8.8t^2 = -2.4
t^2 = -2.4 / -8.8
t^2 = 0.272727
t ≈ √0.272727
t ≈ 0.521 s
So, it will take approximately 0.521 seconds for Tom to hit the ground.
Now, let's find the horizontal distance traveled by Tom before hitting the ground. We know the initial horizontal velocity of Tom is 4.8 m/s.
Using the equation:
distance = velocity × time
distance = 4.8 m/s × 0.521 s
distance ≈ 2.502 m
Therefore, Tom will strike the floor approximately 2.502 meters from the edge of the table.
Next, let's find the speed Tom will have just before hitting the ground.
Using the equation:
final velocity = initial velocity + acceleration × time
Here, the initial velocity is 0 m/s (as Tom slides off the edge) and the acceleration is 9.8 m/s^2 (due to gravity). The time is the same as before, approximately 0.521 seconds.
final velocity = 0 m/s + 9.8 m/s^2 × 0.521 s
final velocity ≈ 5.10 m/s
So, Tom will have a speed of approximately 5.10 m/s just before hitting the ground.