Tom the cat is chasing Jerry the mouse across a table surface 1.4 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?
Your answer was incorrect, but has changed from what was graded. m from the table
What velocity components will he have just before he hits? (Use a coordinate system in which up is positive.)
Your answer was incorrect, but has changed from what was graded. m/s (x direction)
m/s (y direction)
Tom the cat is chasing Jerry the mouse across the surface of a table 1.4 m above 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 5.4 m/s. Where will Tom strike the floor?
To find where Tom will strike the floor, we need to calculate the horizontal and vertical displacements separately.
First, let's calculate the time it takes for Tom to reach the floor using the vertical motion equation:
h = ut + (1/2)gt²
Where:
h = vertical displacement (distance from the table to the floor)
u = initial vertical velocity (0 m/s as Tom slides off the table horizontally)
g = acceleration due to gravity (approximately 9.8 m/s²)
t = time
Since h is given as 1.4 m, we can rearrange the equation to solve for t:
1.4 = (1/2) * 9.8 * t²
2.8 = 9.8 * t²
t² = 2.8 / 9.8
t ≈ √(2.8 / 9.8)
t ≈ 0.588 s (rounded to three decimal places)
Now, let's calculate the horizontal displacement using horizontal motion equation:
s = ut + (1/2)at²
Where:
s = horizontal displacement (distance Tom slides off the edge of the table)
u = initial horizontal velocity (4.8 m/s)
a = horizontal acceleration (0 m/s², as there is no horizontal force acting on Tom)
t = time (0.588 s)
Plugging in the values:
s = 4.8 * 0.588 + (1/2) * 0 * (0.588)²
s ≈ 2.8224 m (rounded to four decimal places)
Therefore, Tom will strike the floor approximately 2.8224 meters away from the edge of the table.
Now let's find the velocity components just before Tom hits the floor.
In the horizontal direction, the velocity will remain constant because there is no horizontal force acting on Tom. Therefore, the horizontal component of the velocity will be 4.8 m/s.
In the vertical direction, we can use the equation:
v = u + gt
Where:
v = final vertical velocity
u = initial vertical velocity (0 m/s as Tom slides off the table horizontally)
g = acceleration due to gravity (approximately 9.8 m/s²)
t = time (0.588 s)
Plugging in the values:
v = 0 + 9.8 * 0.588
v ≈ 5.764 m/s (rounded to three decimal places)
Therefore, just before Tom hits the floor, his velocity components will be:
Horizontal component: 4.8 m/s
Vertical component: -5.764 m/s (negative value indicates downward direction as per the chosen coordinate system)