Marty is sipping a soda while leaning over the railing of a cruise ship that is

Question

Marty is sipping a soda while leaning over the railing of a cruise ship that is cruising at a speed of 7.00 km/h through Alaska's majestic Glacier Bay. One of the ice cubes in Marty's soda falls overboard, and falls 21.0 m to the water below. Marty remains at rest with respect to the ship throughout this process, and the ice cube is initially at rest with respect to Marty when it begins its fall. Neglect air resistance in this process (ice cubes are notoriously slippery). If you need it, use g = 9.80 m/s2. While the ice cube is falling, the ship (and Marty) keep moving in a straight line. What is the horizontal distance between the point where the ice cube hits the water, and the point on the water directly below Marty's soda glass when the cube hits the water?

Explanation / Answer

Consider the Motion of Cube :

Along the Vertical direction :

Voy = initial velocity = 0 m/s

Y = vertical displacement = 21 m

a = acceleration = 9.8 m/s2

t = time

Using the equation

Y = Voy t + (0.5) at2

21 = 0 t + (0.5) (9.8) t2

t = 2.07 sec

Along the Horizontal direction :

X = Horizontal displacement

Vox = velocity in horizontal direction = 7 km/h = 1.94 m/s

t = 2.07 sec

X = Vox t = 1.94 x 2.07 = 4.02 m

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