Question

An object at the top of a stairwell is given a horizontal velocity of m vx = 2.75 m/s . Given that the rise and run (height and depth) of each step is 10cm determine which step the object will hit first

Answer 1

Solution: Let height be "h" and width be "b", "n" is the number of steps and "t" be the time taken.

Now, Horizontal distance (x) = n*b

=> v_x*t = n*b

=> t = n*b/2.75 ( Horizontal velocity = 2.75 m/s = Given)------------------(1)

Vertical distance (y) = v_yt + 1/2 gt²

=> n*h = 0 + 9.8t²/2

Plugging the value of "t" from equation (1)

=> n*h = 9.8*n²b²/(2*2.75²)

=> h = 0.647*n*b²

Since, h = b = 10 cm = 0.1 m, thus, 0.1  = 0.647*n*0.1²

=> n = 15.45. Answer

Ball will strike at 16th step first.