Question

An object rolls off a tabletop with a horizontal velocity (v_0x = 18 , m/s ). The table is at a height (y_0 = 0.65, m ), above the floor.

What's the horizontal distance, in meters, from the edge of the tabletop to where the object lands?
a) 9.0 m
b) 15.6 m
c) 18.0 m
d) 21.6 m

Answer 1

The horizontal distance from the edge of the tabletop to where the object lands is 9.0 m.

Step-by-step explanation:

To find the horizontal distance an object travels when it rolls off a tabletop, we can use the equation:

d = v0x * t

where d is the horizontal distance, v0x is the horizontal velocity, and t is the time of flight. In this case, the horizontal velocity is given as 18 m/s and the object starts at a height of 0.65 m above the floor. Since the object rolls off the table, we can assume it falls freely in the vertical direction. Using the equation for the time of flight of an object in free fall:

t = sqrt(2h/g)

where h is the initial height and g is the acceleration due to gravity (assumed to be 9.8 m/s2), we can calculate the time of flight. Substituting this into the first equation, we can find the horizontal distance:

d = v0x * sqrt(2h/g)

Plugging in the given values:

d = 18 m/s * sqrt(2 * 0.65 m / 9.8 m/s2)

d = 9.0 m

Therefore, the horizontal distance from the edge of the tabletop to where the object lands is 9.0 m.