A box slides off a horizontal desk with a speed of 2.00 m/s. It strikes the floo

Question

A box slides off a horizontal desk with a speed of 2.00 m/s. It strikes the floor in 0.400 s. Ignoring air resistance, what is the height of the desk above the floor? It is always helpful to first indicate direction you are using for positive y-axis. What is the horizontal distance from the edge of the desk to the point where the box strikes the floor in problem 2 above? What is the magnitude and direction of the box's velocity in problem 2, just before the box reaches the floor? Always give direction relative so that anyone knows the quadrant.

Explanation / Answer

Here ,

speed , u = 2 m/s

time taken , t = 0.40 s

2) height of the desk = 0.50 g * t^2

height of the desk = 0.50 * 9.8 * 0.40^2

height of the desk = 0.78 m

3)

horizontal distance = horizontal speed * time of flight

horizontal distance = 2 * 0.40

horizontal distance = 0.80 m/s

4)

magnitude of box' velocity is v

Using third equation of motion

v^2 - 2^2 = 2 * 9.8 * 0.78

v = 4.39 m/s

the magnitude of box's velocity is 4.39 m/s

theta = arctan(0.40 * 9.8/2) = 63 degree

the direction of box's velocity is 63 degree below horizontal

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