Solving Acceleration Problem: Time & Distance Calculations

[gztiger]

Homework Statement

The surface of a table is 0:8 m above the floor. A marble rolls o the edge of the
table. The acceleration due to gravity at the surface of the Earth is g = 10 m=s2.

Homework Equations

I am not sure about the equation, it was not given.

The Attempt at a Solution

a. How much time does the marble take to go from the edge of the table
to the floor?
b. The speed the marble rolls is 2 m=s. How far does the marble travel
horizontally, after it rolls o the table?

 

[rl.bhat]

Hi gztiger, welcome to PF1) y = yo + vo*t - 1/2*gt^2
2) Horizontal velocity does not change due to gravity.

 

[tomcue]

To solve these problems, we can use the equation d = v0t + 1/2at^2, where d is the distance traveled, v0 is the initial velocity, a is the acceleration, and t is the time.

a. To find the time it takes for the marble to reach the floor, we can solve for t using the given values:

d = 0.8 m (since the marble starts at the edge of the table and falls to the floor)
v0 = 0 m/s (since the marble is initially at rest)
a = 10 m/s^2 (acceleration due to gravity)

Plugging these values into the equation, we get:

0.8 = 0 x t + 1/2 x 10 x t^2
0.8 = 5t^2
t^2 = 0.16
t = √0.16 = 0.4 seconds

Therefore, it takes the marble 0.4 seconds to reach the floor.

b. To find the horizontal distance traveled by the marble, we can use the equation d = vt, where d is the distance, v is the velocity, and t is the time. We are given that the speed of the marble is 2 m/s, so:

d = 2 m/s x 0.4 s = 0.8 m

Therefore, the marble travels 0.8 meters horizontally after rolling off the table.