Question

(Go go gadget problem solver!) Joe, Bill, and Fred are playing a game with marbles at the top of an uncarpeted (wooden) staircase. They decide to try to roll their marbles off the top step and see how many steps the marble will skip before hitting. The faster they roll the marbles, the farther down the staircase the marble will go before hitting a step. Suppose one of these marbles leaves the floor at the top of the staircase at 2.54m/s. Each stair is 20.0cm tall and 20.0cm deep. Which stair will the marble hit first? Clearly label your answer on a picture/sketch. [Hint, you don

Answer 1

marble touches the seventh stair.

let t is the time taken to travel first stair(20 cm) in y-direction

h1 = 0.5*g*t^2

t = sqrt(2*h1/g)

= sqrt(2*0.2/9.8)

= 0.202 s

x = vx*t

= 2.54*0.202

= 0.513, so, marble does not touch first stiar.

let t is the time taken to travel second stair(40 cm) in y-direction

h2 = 0.5*g*t^2

t = sqrt(2*h2/g)

= sqrt(2*0.4/9.8)

= 0.286 s

x = vx*t

= 2.54*0.286

= 0.726, so, marble does not touch seond stiar.

let t is the time taken to travel third stair(60 cm) in y-direction

h1 = 0.5*g*t^2

t = sqrt(2*h1/g)

= sqrt(2*0.6/9.8)

= 0.235 s

x = vx*t

= 2.54*0.35

= 0.89, so, marble does not touch third stiar.

let t is the time taken to travel fourth stair(80 cm) in y-direction

h1 = 0.5*g*t^2

t = sqrt(2*h1/g)

= sqrt(2*0.8/9.8)

= 0.404 s

x = vx*t

= 2.54*0.404

= 1.02, so, marble does not touch fourth stiar.

let t is the time taken to travel fifth stair(100 cm) in y-direction

h1 = 0.5*g*t^2

t = sqrt(2*h1/g)

= sqrt(2*1/9.8)

= 0.452 s

x = vx*t

= 2.54*0.452

= 1.15, so, marble does not touch fifth stiar.

let t is the time taken to travel six stair(120 cm) in y-direction

h1 = 0.5*g*t^2

t = sqrt(2*h1/g)

= sqrt(2*1.2/9.8)

= 0.495 s

x = vx*t

= 2.54*0.495

= 1.26, so, marble does not touch sixth stiar.
let t is the time taken to travel seventh stair(140 cm) in y-direction

h1 = 0.5*g*t^2

t = sqrt(2*h1/g)

= sqrt(2*1.4/9.8)

= 0.534 s

x = vx*t

= 2.54*0.0.534

= 1.34 m

here 1.34m < 1.4 m. so, marble touchs the seventh stiar.