tom the cat is chasing jerry the mouse across the table surface at 1.5 m high, jerry steps out of the way and tom slides off the table at 5m/s. Where will tom hit the floof and what are the velocity components just before impact

1.5 = 4.9t^2

t = .55s

Vy = -9.8(.55) = -5.39
Vx = 5.00

Tom will hit the floor at x=5(.55) = 2.75

assuming the +x direction is the direction of travel across the table.

To determine where Tom will hit the floor and the velocity components just before impact, we need to analyze the vertical and horizontal motion separately.

Horizontal Motion:
Since Jerry steps out of the way, there is no horizontal force acting on Tom during his fall. As a result, there is no horizontal acceleration, and Tom will continue to move horizontally at a constant velocity. Therefore, the horizontal velocity component just before impact will be the same as it was just before Tom slid off the table, which is 5 m/s.

Vertical Motion:
Tom's vertical motion can be analyzed using the equations of motion under constant acceleration, assuming the gravitational acceleration is 9.8 m/s^2. We can use the following equation:

h = ut + (1/2)at^2,

where:
h = vertical distance traveled (1.5 m)
u = initial vertical velocity (0 m/s, since Tom starts from rest)
a = vertical acceleration (-9.8 m/s^2)
t = time of flight (unknown)

We need to solve this equation for t. Putting in the known values, we have:

1.5 = 0 + (1/2)(-9.8)t^2

Rearranging the equation:

4.9t^2 = 1.5

t^2 = 1.5 / 4.9
t^2 ≈ 0.3061

Taking the square root:

t ≈ √0.3061
t ≈ 0.5539 seconds

Now, we know that Tom falls for approximately 0.5539 seconds. Using this time, we can calculate the vertical component of his velocity just before impact:

v = u + at,

where:
v = final vertical velocity at impact (unknown)
u = initial vertical velocity (0 m/s)
a = vertical acceleration (-9.8 m/s^2)
t = time of flight (0.5539 seconds)

v = 0 + (-9.8)(0.5539)
v ≈ -5.43 m/s

The negative sign indicates that Tom's velocity is directed downwards.

Putting it all together:
Tom will hit the floor with a vertical velocity of approximately -5.43 m/s and a horizontal velocity of 5 m/s. The direction of the horizontal velocity will depend on the direction in which Tom was sliding off the table.