Calculate the predicted impact point of a marble rolling off a desk w/ the height of .757m and traveling at an avg. velocity of .8231 m/s?
how long does it take to fall .757m? 1/2 gt^2 = .757
horizontally, distance = speed * time
that "avg velocity" junk is meaningless. What you need is the speed just as it rolls off the table, right?
Wouldn't it be vertical motion though?
t=1.34 seconds?
the avg velocity I think is horizontal speed on the table.
time to fall: 1/2 g t^2=757 or t= .395sec (check that).
how far did it travel horizontally? d=horizonal speed*time=.8231*.395= 32.5 cm
To calculate the predicted impact point of a marble rolling off a desk, you need to consider the projectile motion of the marble. Here's how you can calculate it:
1. Determine the time of flight:
The time of flight is the total time it takes for the marble to reach the ground from the desk. To find it, you can use the formula:
π‘ = β(2β/π)
where:
π‘ = time of flight
β = height of the desk (0.757m)
π = acceleration due to gravity (approximately 9.8 m/sΒ²)
Substituting the values into the formula:
π‘ = β(2 * 0.757 / 9.8)
2. Calculate the horizontal distance:
The horizontal distance is the distance the marble travels horizontally during the time of flight. Since the marble is rolling off the desk with an average velocity, the horizontal distance can be determined by multiplying the average velocity by the time of flight:
π = π£ Γ π‘
where:
π = horizontal distance
π£ = average velocity (0.8231 m/s)
π‘ = time of flight (calculated in step 1)
Substituting the values into the formula:
π = 0.8231 Γ π‘
Now, you can substitute the value of π‘ you calculated in step 1 to find the horizontal distance π.
Keep in mind that this calculation assumes no air resistance, and the marble behaves as a projectile in free fall.