Tom the cat is chasing Jerry the mouse across a table surface 2.3 m off the floor. Jerry steps out of the way last second, and Tom slides off the edge of the table at a speed of 7.7 m/s. Acceleration due to gravity is 9.8 m/s^2. What speed will Tom have just before he hits?
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Find the x- and y-component of his speed separately, then combine them to get the actual resultant speed.
X-component
The x-component of the speed will be 7.7 m/s just before he hits. That's because there is no acceleration/deceleration in the x-direction, so the speed must remain constant.
Y-component.
The y-component of the speed starts off at 0 m/s right when he slides off the table. He accelerates downward at 9.8 m/s² and falls 2.3 m.
v₂² = v₁² + 2ad
v₂² = 0² + 2(9.8)(2.3)
v₂² = 45.08
Now find the magnitude of the final speed.
v = √(vx² + vy²)
v = √(7.7² + 45.08)
v = 10.216 m/s
X-component
The x-component of the speed will be 7.7 m/s just before he hits. That's because there is no acceleration/deceleration in the x-direction, so the speed must remain constant.
Y-component.
The y-component of the speed starts off at 0 m/s right when he slides off the table. He accelerates downward at 9.8 m/s² and falls 2.3 m.
v₂² = v₁² + 2ad
v₂² = 0² + 2(9.8)(2.3)
v₂² = 45.08
Now find the magnitude of the final speed.
v = √(vx² + vy²)
v = √(7.7² + 45.08)
v = 10.216 m/s