Tom the cat is chasing Jerry the mouse across the surface of atable 1.5 m above

Question

Tom the cat is chasing Jerry the mouse across the surface of atable 1.5 m above the floor. Jerry steps out of the way at the lastsecond, and Tom slides off the edge of the table at a speed of 5.0m/s. Where will Tom strike the floor, and what velocity componentswill he have just before he hits? I know you need two sets of equations (one set for the x-axisand one set for the Y-axis) but I don't undertand how you derivethe equations needed. Tom the cat is chasing Jerry the mouse across the surface of atable 1.5 m above the floor. Jerry steps out of the way at the lastsecond, and Tom slides off the edge of the table at a speed of 5.0m/s. Where will Tom strike the floor, and what velocity componentswill he have just before he hits? I know you need two sets of equations (one set for the x-axisand one set for the Y-axis) but I don't undertand how you derivethe equations needed.

Explanation / Answer

To find this you do need two equations, one for horizontal and onefor vertical. The horizontal equation is pretty easy. f(x)=5x for position andf(x)=5 for horizontal velocity. The Vertical is a little bit more challenging but not to bad. Just start by writing the equation for velocity. He starts atzero and accelerates at 9.8m/s^2 until he hits the ground... so theequation would be f(x)=9.8x for velocity. For verticalposition you have to integrate the velocity formula and substitute1.5 for the C value. So f(x)= (9.8/2)x^2+1.5 .... is yourposition vs time graph for your vertical component. So... to solve this first take the vertical position graph and findthe point at which it hits the x axis... this will be the time hehits the ground... or t. So armed with the time, you can thenplug that into your horizontal velocity equation to find thedistance from the table he will be when he hits(y=5*t). The last part is you take the horizontal velocity component (5m/s)and your vertical velocity component (your velocity equation withyour time you found earlier plugged into x... y=9.8(t)) and youhave your two components. Good luck and come back if you need any more help.

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