In her physics lab, Jessica rolls a 20-g marble down a ramp and off the table with a horizontal velocity of 1.10 m/s. The marble falls in a cup placed 0.44 m from the table's edge. Find the table's height. Use g = 10. m/s2. Enter m as unit.
X = V*t = 0.44 m.=Hor. dist from table.
1.1*t = 0.44
Tf = 0.4 s. = Fall time or time in air.
h = Vo*t + 0.5g*t^2.
h = 0 + 5*0.4^2 = 0.8 m.
To find the table's height, we need to use the equation of motion for the horizontal motion of the marble.
First, let's define the variables:
m = mass of the marble = 20 g = 0.02 kg (convert grams to kilograms)
v = horizontal velocity of the marble = 1.10 m/s
d = horizontal distance traveled by the marble = 0.44 m
g = acceleration due to gravity = 10 m/s^2
Now, let's use the formula:
d = v * t
Since the horizontal velocity remains constant, the time it takes for the marble to travel the distance d is the same as the time it takes for the marble to fall vertically.
We can use the formula for the vertical motion of the marble:
h = (1/2) * g * t^2
where h is the height of the table and t is the time taken for the marble to fall.
Rearranging the equation, we can get t in terms of h:
t = sqrt(2h / g)
Now, we can substitute the value of t in the equation for horizontal motion:
d = v * sqrt(2h / g)
Solving for h:
h = (d^2 * g) / (2 * v^2)
Now, plug in the given values:
d = 0.44 m
g = 10 m/s^2
v = 1.10 m/s
h = (0.44^2 * 10) / (2 * 1.10^2)
Calculating this expression, we find:
h ≈ 0.0804 m
Therefore, the table's height is approximately 0.0804 meters.