Object drops vertically with a horizontal force acting on it

[MechaMZ]

Homework Statement

A couch cushion of mass m is released from rest at the top of a building having height h. A wind blowing along the side of the building exerts a constant horizontal force of magnitude F on the cushion as it drops as shown in the figure. The air exerts no vertical force.

http://img3.imageshack.us/img3/5868/p563.gif

If m = 1.22 kg, h = 8.48 m, and F = 2.42 N, how far from the building will the cushion hit the level ground?

Homework Equations

F=ma
x_f-x_i = v_it+0.5at²

The Attempt at a Solution

The time take for this situation should not be the same as an object is dropping vertically downward with 1.22kg, since there is a horizontal force acting on the current situation.
So I can't take the time as a common variable in between the free fall and this situation, but how to find out the variables?
the correct answer is 1.72 m

 

[Fightfish]

The time take for this situation should not be the same as an object is dropping vertically downward with 1.22kg, since there is a horizontal force acting on the current situation.
So I can't take the time as a common variable in between the free fall and this situation, but how to find out the variables?

Unfortunately, the time taken is the same, as the vertical and horizontal velocities are independent of each other. Whether the object is moving towards the right or left with whatever velocity does not change or affect the vertical motion of the object.

 

[tomcue]

I would approach this problem by breaking it down into its individual components and applying the relevant equations to each component.

First, I would consider the vertical motion of the cushion. Since there is no vertical force acting on the cushion, it will experience free fall and its motion can be described by the equation xf-xi = vit+0.5at^2. Here, xf represents the final position (ground level) and xi represents the initial position (top of the building). We can rearrange this equation to solve for t, the time it takes for the cushion to reach the ground: t = √(2h/g), where g is the acceleration due to gravity. Plugging in the given values, we get t = √(2(8.48 m)/9.8 m/s^2) = 1.47 seconds.

Next, I would consider the horizontal motion of the cushion. Here, we can use the equation F=ma, where F is the horizontal force, m is the mass of the cushion, and a is the acceleration. We can rearrange this equation to solve for a: a = F/m. Plugging in the given values, we get a = 2.42 N/1.22 kg = 1.98 m/s^2.

Now, we can use the equation xf-xi = vit+0.5at^2 to calculate the horizontal distance the cushion travels during the 1.47 seconds it takes to reach the ground. Here, xf represents the final horizontal position (distance from the building) and xi represents the initial horizontal position (zero). Plugging in the values we calculated for t and a, we get xf = 0 + (1.98 m/s^2)(1.47 s)^2/2 = 2.42 m.

Therefore, the cushion will hit the ground at a horizontal distance of 2.42 m from the building, as the correct answer stated.