This question had been asked for many times and I've read the solution and did it myself.
Tom the cat is chasing Jerry the mouse across a table surface 1.5 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 5.0 m/s. Where will Tom strike the floor, and what velocity components will he have just before he hits?
I just don't get the question that well. Aren't we taught that the x component doesn't matter? Then why did we use the velocity (5.0m/s) to find out the values...etc?
I just learned about projectile motion today and it was pretty complicated...thank you.
The velocity Tom had in the x direction determines how far away from the base of the table Tom lands. If he simply stepped off he would land at the base of the table. But if he has a velocity, he will land some distance from the base.
I understand that projectile motion can be confusing, but let's break down the question and the reasoning behind using the velocity (5.0 m/s) to find the values.
In this scenario, Tom the cat slides off the edge of the table with an initial velocity of 5.0 m/s. The question asks where Tom will strike the floor and what velocity components he will have just before he hits.
When an object is in projectile motion, it follows a curved path under the influence of gravity, assuming no other forces are acting on it. The motion can be divided into two components: horizontal (x-direction) and vertical (y-direction).
While it is true that the x-component of the velocity does not affect the time of flight or the vertical motion, it does affect the horizontal distance traveled. In this case, since Tom slides off the table horizontally, the x-component of his velocity is relevant.
To solve this problem, we need to consider the vertical motion of Tom. Since he starts with an initial velocity of 5.0 m/s in the x-direction and falls freely in the y-direction due to gravity, we can use equations of motion to determine the time of flight and the vertical displacement.
Using the equation y = y0 + v0y * t + 1/2 * g * t^2, where y is the vertical displacement, y0 is the initial height (1.5 m), v0y is the initial vertical velocity (which is 0 m/s since the vertical velocity at the start is 0 in this case), g is the acceleration due to gravity (-9.8 m/s^2), and t is the time of flight, we can calculate the time it takes for Tom to hit the ground.
Next, we can use the equation x = x0 + v0x * t, where x is the horizontal distance traveled, x0 is the initial horizontal position (which is also 0 in this case), v0x is the initial horizontal velocity (which is 5.0 m/s), and t is the time of flight to calculate the horizontal distance.
The point where Tom strikes the floor will have a horizontal distance (x-coordinate) from the table edge and a vertical displacement (y-coordinate) below the table surface. These values can be found using the equations mentioned above.
Finally, to determine the velocity components just before Tom hits the floor, we can use the equations of motion. The x-component of the velocity will remain constant at 5.0 m/s since there is no horizontal force acting on Tom. The y-component of the velocity will change due to acceleration from gravity and can be calculated using the equation v = v0 + g * t, where v is the final vertical velocity and v0 is the initial vertical velocity.
By plugging in the calculated values of time and initial velocities into the equations mentioned above, we can find the x and y velocity components just before Tom hits the floor.
So, to summarize, we need to consider the x-component to find the horizontal distance traveled by Tom. We can use the equations of motion to calculate the time of flight and vertical displacement. The point of impact can be found by combining the horizontal distance and vertical displacement. Finally, the velocity components just before hitting the floor can be determined by considering the x and y motion separately.