A roach that runs for its life because you try to hit it with your physics book runs off the horizontal tabletop with a speed of 0.582 m/s. It strikes the floor a horizontal distance 0.315 m away from the edge of the table. Ignore air resistance.
What will be the vertical component of the roach's velocity just before it hits the floor?
(define positive y upward)
Dx = Xo * Tf = 0.315 m.
0.582 * Tf = 0.315
Tf = 0.541 s. = Fall time or time in air
Y = Yo + g*t = 0 + 9.8*0.541 = 5.30 m/s.
= Ver. component of final velocity.
To find the vertical component of the roach's velocity just before it hits the floor, we can use the equations of motion for free-falling objects.
First, we need to determine the time it takes for the roach to fall from the edge of the table to the floor. Since there is no initial vertical velocity and we can ignore air resistance, we can use the equation:
y = (1/2) * g * t^2
Here, y is the vertical distance from the edge of the table to the floor (0.315 m) and g is the acceleration due to gravity (-9.8 m/s^2). Solving for t, we get:
t = sqrt((2 * y) / g)
Next, we can determine the roach's vertical velocity just before it hits the floor using the equation:
v = g * t
Here, v is the vertical component of the roach's velocity. Plugging in the values, we get:
v = -9.8 * sqrt((2 * 0.315) / -9.8)
Simplifying this expression, we find:
v ≈ -0.737 m/s
Since upward is defined as positive in this case, the vertical component of the roach's velocity just before it hits the floor is approximately -0.737 m/s.