A marble rolls off a table with a speed of 2.30 m/s. If the table is 1.12 m high, how far from the

base of the table does the marble land? (Find the time in the air first.)

1.10 m

Explanation:

First, find the time it takes to land.

Given, in the y direction:

Δy = 1.12 m

v₀ = 0 m/s

a = 9.8 m/s²

Find: t

Δy = v₀ t + ½ at²

(1.12 m) = (0 m/s) t + ½ (9.8 m/s²) t²

t = 0.478 s

Next, find the distance traveled in that time.

Given, in the x direction:

v₀ = 2.30 m/s

a = 0 m/s²

t = 0.478 s

Find: Δx

Δx = v₀ t + ½ at²

Δx = (2.30 m/s) (0.478 s) + ½ (0 m/s²) (0.478 s) ²

Δx = 1.10 m