A marble rolls off a lab table that is 0.92 m high. It rolls off the table with a velocity of 1.66 m/s. How far from the base of the table must the chip be placed so that the marble will hit the chip?

h = 0.5g*t^2 = 0.93 m.

4.9t^2 = 0.92
t^2 = 0.1878
Tf = 0.433 s.

Dx = Xo*Tf = 1.66m/s * 0.433s = 0.719 m.

To solve this problem, we can use the equations of motion to calculate the horizontal distance the marble will travel before hitting the chip.

The key equation we need is the horizontal motion equation:

d = v*t

where:
- d is the horizontal distance,
- v is the horizontal velocity of the marble, and
- t is the time it takes for the marble to fall from the table.

To find the time of fall, we can use the equation for vertical motion:

h = (1/2)*g*t^2

where:
- h is the vertical height of the table, and
- g is the acceleration due to gravity.

Given:
- h = 0.92 m
- v = 1.66 m/s
- g = 9.8 m/s^2 (approximate value)

Let's calculate the time it takes for the marble to fall:
Using the equation for vertical motion:
0.92 = (1/2)*9.8*t^2
Simplifying the equation:
t^2 = (2*0.92)/9.8
t^2 ≈ 0.188
t ≈ √0.188
t ≈ 0.434 s (approximate value)

Now, we can use the equation for horizontal motion to find the distance the marble will travel:
d = v*t
d = 1.66 * 0.434
d ≈ 0.72 m (approximate value)

Therefore, the chip should be placed approximately 0.72 meters from the base of the table so that the marble will hit it.

To answer this question, we need to consider the concept of projectile motion and apply the equations of motion.

First, we need to find the time it takes for the marble to fall from the table to the ground. We can use the equation:

h = (1/2) * g * t^2

Where:
h: height of the table (0.92 m)
g: acceleration due to gravity (9.8 m/s^2)
t: time

Rearranging the equation, we get:

t^2 = (2 * h) / g

t^2 = (2 * 0.92) / 9.8
t^2 ≈ 0.188

Taking the square root of both sides, we find:

t ≈ √0.188
t ≈ 0.434 s

Now, we need to find the horizontal distance traveled by the marble during this time. Since there is no external force acting horizontally on the marble, its horizontal velocity remains constant. Therefore, we can use the equation:

d = v * t

Where:
d: horizontal distance
v: horizontal velocity (1.66 m/s)
t: time (0.434 s)

Substituting the values, we have:

d = 1.66 * 0.434
d ≈ 0.718 m

Therefore, the chip should be placed approximately 0.718 meters from the base of the table so that the marble will hit it.