Tom the cat is chasing Jerry the mouse on a table. Jerry puts on the brakes and stops and Tom continues right off the edge of the table at 4.00 m/s. If it takes Tom 0.50 seconds to hit the ground, then the table is approximately ____ meters high and Tom hit the ground a horizontal distance of ____ meters from the table"s edge. (Note: Numbers are randomized numbers and likely different from the numbers listed here.)

54

To calculate the height of the table, we can use the formula for the distance traveled in free fall:

distance = 0.5 * acceleration * time^2

Given that Tom took 0.50 seconds to hit the ground and the acceleration due to gravity is approximately 9.8 m/s^2, we can plug these values into the formula to find the distance traveled vertically:

distance = 0.5 * 9.8 * (0.50)^2
distance = 0.5 * 9.8 * 0.25
distance = 1.225 meters

Therefore, the table is approximately 1.225 meters high.

To calculate the horizontal distance Tom traveled, we can use the formula for distance traveled with constant velocity:

distance = velocity * time

Given that Tom's velocity was 4.00 m/s and he took 0.50 seconds to hit the ground, we can calculate the horizontal distance traveled:

distance = 4.00 * 0.50
distance = 2.00 meters

Therefore, Tom hit the ground a horizontal distance of 2.00 meters from the table's edge.

To determine the height of the table and the horizontal distance Tom falls from the edge of the table, we can use the equations of motion in projectile motion.

First, let's analyze the vertical motion of Tom when he falls off the table. We know that the initial vertical velocity (vy) is 0 m/s since Tom is not jumping up or down when he falls. The time of flight (t) is given as 0.50 seconds.

The general formula for vertical displacement is given by the equation:
Δy = vy * t + (1/2) * a * t^2

Since Tom is falling vertically, acceleration due to gravity (g) is acting downwards, making the value negative. We can substitute the values into the equation. Here, Δy represents the height of the table.

0 = 0 * 0.50 + (1/2) * (-9.8) * (0.50^2)
0 = 0 - 1.225 * 0.25
0 = -0.30625

So, the vertical displacement is approximately -0.30625 meters. Since the displacement is negative, it means Tom falls downwards, which makes sense.

Now, let's analyze the horizontal motion of Tom when he falls off the table. We know that the initial velocity in the x-direction (vx) is 4.00 m/s, and we need to find the horizontal distance (Δx) Tom travels before hitting the ground.

The formula for horizontal displacement is given by the equation:
Δx = vx * t

Substituting the values into the equation:
Δx = 4.00 * 0.50
Δx = 2.00

So, Tom hits the ground a horizontal distance of approximately 2.00 meters from the table's edge.

Therefore, the table is approximately 0.30625 meters high and Tom hits the ground a horizontal distance of approximately 2.00 meters from the table's edge.