Answer:

Vx = 1.50 m/s ; height of table = ? ; dx = 0.70 m ; v_final = ?

Formula for horizontal motion

dx = Vx * t_fall

0.70 m = 1.50 m/s * t_fall

t_fall = 0.70 m / 1.50 m/s

t_fall = 0.467 seconds

Solving for the height of the table top

height = 1/2 * g * t_fall^2

height = 4.9 m/s^2 * (0.467 s)^2

height = 4.9 m/s^2 * 0.218 s^2

height = 1.068 meters

Solving for the marble's velocity before hitting the floor

The marble's velocity has two components that must be combined by using the Pythagorean theorem

v^2 = Vx^2 + Vy^2

v^2 = (1.50 m/s)^2 + Vy^2

v^2 = 2.25 (m/s)^2 + g * t_fall

v^2 = 2.25 (m/s)^2 + 9.8 m/s^2 * 0.467 s

v^2 = 2.25 (m/s)^2 + (4.577 m/s)^2

v^2 = 2.25 (m/s)^2 + 20.95 (m/s)^2

v^2 = 23.2 (m/s)^2

v = √(23.2) (m/s)^2

v_final = 4.82 m/s at 65 degrees from the horizontal

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