A marble is rolled so that it is projected horizontally off the top landing on the staircase?

Question

initial speed of the marble is 3.0meters/second. Each step is .18 meters high and .30 meters wide. Which step does the marble strike first? (The answer given is "step 4", but I need to know how- using the kinematic equation)

Answer 1

Lol, I have a physics test tomorrow so I better be able to do this.


Ok, the ratio of stair height and width is .18/.30

This is also the ratio of Y position over X position.

Now, X(t) = x0 + vt + 1/2at^2; x0= 0, 1/2at^2 = 0 because it starts at origin and has no acceleration. vt = 3

Y(t) = y0 + vt+ -1/2gt^2; y=0 vt = 0 but g = 9.8

ratio = Y(t)/X(t) = 4.9t^2/3t; Solve for T. That is the time when it hits a staircase. T = .3673

now, after you find T, you know that 3t= x position displaced by particle movement. You also know the width of each step.

plug t into 3t and then divide by width of the steps. Round Up to whatever whole number is closest and that should equal 4.

3.67 meters from origin..round up to 4.

Answer 2

The assumption is that the horizontal velocity does not change

Vx = 3 m/s

x horizontal distance is x = Vx(time)

The vertical velocity is the result of gravity 9.8 m/s^2

Vy = - 9.8 (time)

y = (1/2) (-9.8) (time^2)

time required to clear first step is .3/3 1/10 sec

You can arrange the formula's based on the number of steps and solve them simultaneously or work it out step by step.

Answer 3

If the guy is leaping off the form in a vacuum... The time it may take him to hit the floor could be resembling sqrt((hight*2)/(accelloration)) =time so if the form is 70 ft severe and the acceloration of gravity grew to develop into 33ft/s^2, it may take precise at 2 seconds to hit the floor. if he grew to develop into working around the form at finished velocity, say 20 ft/2d (~13 miles consistent with hour), he could land ~40 ft from the form. The mass of the guy does no longer count selection. Now in case you prefer to speak suited to the impulse jointly as he hits the floor it particularly is exciting. Impulse = mass * velocity. which skill a one hundred ninety lbs guy could hit the floor going 66 ft consistent with 2d (40 5 miles/hour). which skill he could hit the floor with ~ 12000 lbs of stress! that would harm. If the guy jumps off an easily shape in the international with an ecosystem, many things could substitute. Is he leaping into the wind or with it?