Question

A marble is fired horizontally with an initial velocity of 2.5 m/s from a table that is 0.8 m high. How far will the marble travel along the floor before it lands?

Answer 1

The marble will travel 1.0 meter along the floor before it lands.

Step-by-step explanation:

To find the horizontal distance the marble will travel before it lands, we need to find the time it takes for the marble to land. We can use the equation:

d = v*t

Where:

d is the horizontal distance

v is the initial velocity in the horizontal direction

t is the time of flight

Since the marble is fired horizontally, the vertical component of velocity is 0. Therefore, it will take the same time for the marble to land as it would take for an object to fall from a height of 0.8 m. We can calculate the time using the equation:

t = sqrt(2h/g)

Where:

h is the height of the table

g is the acceleration due to gravity

Using the given values, the time of flight is: t = sqrt(2 * 0.8 / 9.8) = 0.4 s

Now, we can substitute the time into the first equation to find the horizontal distance:

d = v * t

d = 2.5 * 0.4 = 1.0 m

Therefore, the marble will travel 1.0 meter along the floor before it lands.