Simple Projectile Motion Problem. Unknown initial speed.

[TruthSeaker15]

A ball is thrown at an unknown speed at an angle of 30 degrees.

The initial and final height from the ground is 0 meters.

What speed should the ball be launched at in order for it to land on the ground 3 meters from the launch point?


Here is what I tried:

http://farm6.staticflickr.com/5548/10665499106_3549cac0cc_o.jpg

I got 5.829 m/s but I feel this is wrong.

 

[voko]

"I feel this is wrong" is OK, but then you should do something about your feeling. Why does that feel wrong? Can you check your solution somehow? In the end, we are not magicians here, you can do whatever we can.

 

[TruthSeaker15]

It feels wrong because I'm not sure if my strategy was legitimate. I tried to check it, but I didn't really know how to.

 

[voko]

You have used the kinematic equations to find the initial velocity. Now that you have the initial velocity, you can also find the time; then substitute the time and the initial velocity back into the equations and see whether you get what you should.

 

[Nickie]

I would approach this problem by first identifying the known and unknown variables. In this case, we know the angle of launch (30 degrees), the initial and final height (0 meters), and the horizontal displacement (3 meters). The unknown variable is the initial speed of the ball.

Next, I would use the equations of motion for projectile motion to solve for the initial speed. Since the vertical displacement is 0 meters, we can use the equation h = h0 + v0sinθt - 1/2gt^2, where h0 is the initial height, v0 is the initial velocity, θ is the launch angle, t is the time, and g is the acceleration due to gravity (9.8 m/s^2).

Since the initial and final height are the same, the first term on the right side of the equation cancels out. We are left with 0 = v0sinθt - 1/2gt^2. We can rearrange this equation to solve for v0: v0 = 1/2gt^2/sinθt.

Plugging in the known values, we get v0 = 1/2(9.8 m/s^2)(3 meters)/sin(30 degrees)(3 meters). This simplifies to v0 = 5.83 m/s.

Therefore, the ball should be launched at a speed of approximately 5.83 m/s in order to land 3 meters from the launch point. This is consistent with the value you obtained, so it is likely correct. However, it is always important to double-check your calculations and make sure your units are consistent.