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.)
h=1.5
d=2
Well, well, well! Tom definitely had a "falling with style" moment, didn't he? Let's do some calculations and figure out just how high that table is and how far Tom went off track!
First, let's find the height of the table. We know Tom fell for 0.50 seconds, and we have his final vertical velocity of 4.00 m/s. Remember, we're going to ignore any air resistance because we're dealing with a cartoon world here.
Using the formula h = (1/2) * g * t^2, where h is the height, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time, we can calculate it.
h = (1/2) * 9.8 m/s^2 * (0.50 s)^2
h = 1.225 m
So, the table is approximately 1.225 meters high. Don't worry; the fall isn't too steep! Now, onto the horizontal distance!
Tom was moving horizontally when he fell, and since there was no horizontal force acting on him, his horizontal velocity remained constant. Let's assume Tom's horizontal velocity is Vx m/s.
The horizontal distance he traveled can be calculated using the formula distance = velocity * time.
distance = 4.00 m/s * 0.50 s
distance = 2.00 m
So, Tom hit the ground approximately 2.00 meters from the table's edge. Looks like he went on a little unplanned detour!
Now, keep in mind that these numbers are random; in reality, Tom and Jerry might have different plans for their table adventures!
To find the height of the table, we can use the kinematic equation:
h = (1/2)gt^2
Where:
h = height of the table (unknown)
g = acceleration due to gravity (9.8 m/s^2, assuming we are on Earth)
t = time taken by Tom to hit the ground (0.50 seconds)
Let's solve for h:
h = (1/2) * 9.8 * (0.50)^2
h = (1/2) * 9.8 * 0.25
h = 1.225 meters
Therefore, the table is approximately 1.225 meters high.
To find the horizontal distance Tom hits the ground from the table's edge:
d = v * t
Where:
d = horizontal distance traveled by Tom (unknown)
v = velocity of Tom (4.00 m/s, given in the problem)
t = time taken by Tom to hit the ground (0.50 seconds)
Let's solve for d:
d = 4.00 * 0.50
d = 2.00 meters
Therefore, Tom hits the ground a horizontal distance of approximately 2.00 meters from the table's edge.
h = (1/2)g t^2 = 4.9 (.25)
d = u t = 4 * .5