Problems with finding initial velocity of an object

[lGLOVEl]

Homework Statement

In the figure below, what is the minimum initial speed of the dart if it is to hit the monkey before the monkey hits the ground, which is 12.2 m below the initial position of the monkey, if x is 48 m and h = 11 m? (Ignore any effects due to air resistance.)
Use this figure: http://imgur.com/xDVaz
From my calculations I have that it takes 1.6s for the monkey to fall 12.2m.

Homework Equations

x=X0 + V0t + 1/2(a)(t^2)

The Attempt at a Solution

Im stuck :/

 

[lGLOVEl]

http://imgur.com/xDVaz
Here is the figure the question is talking about

 

[vela]

Why wouldn't the dart reach the monkey in time?

 

[azizlwl]

The time for the dart traveled horizontally distance of x = time the dart traveled up distance of h = time travelled by the monkey downward to height of h

 

[Nickie]

As a scientist, it is important to approach problems like this with a systematic and analytical mindset. The first step would be to clearly define the problem and identify what information is given and what is being asked for. In this case, we are given the distance (x) and height (h) of the monkey, and we are being asked to find the minimum initial speed (V0) of the dart.

Next, we can use the given equation x=X0 + V0t + 1/2(a)(t^2) to create an equation that relates all the known variables. In this case, we can set X0 (initial position) to be 0, since we are only interested in the distance the dart travels. We can also set a (acceleration) to be the acceleration due to gravity, which is -9.8 m/s^2. This leaves us with the equation x=V0t + 1/2(-9.8)(t^2).

Now, we can use the given information about the monkey's fall time to solve for t. Since we know that it takes 1.6 seconds for the monkey to fall 12.2m, we can set the equation 12.2=1/2(-9.8)(1.6^2) and solve for t. This gives us a value of t=1.4 seconds.

Finally, we can plug this value of t into our original equation to solve for V0. This gives us the equation x=V0(1.4) + 1/2(-9.8)(1.4^2). Solving for V0, we get a minimum initial speed of approximately 23.5 m/s for the dart to hit the monkey before it hits the ground.

In conclusion, the key to finding the initial velocity in this problem is to systematically use the given information and equations to solve for all the unknown variables. It is also important to carefully consider the assumptions made, such as ignoring air resistance in this case.