Finding the initial speed of two balls.

[zim70094]

Homework Statement

Ball A is thrown straight upward and returns to its original level in 2 seconds. Ball B is thrown at a 40 degree angle above the horizontal and also returns to its original level in 2 seconds. What is the initial speed of each ball.

Homework Equations

ΔV=at
ΔX=Vit+1/2at^2
v^2-Vi^2=2a(ΔX)
ΔX=1/2(V+Vi)t

The Attempt at a Solution

for ball A I replaced acceleration with gravity and tried to find Vi with the first equation a=-9.81 and t=2s but I didn't know what to do with Vf. I thought maybe it was zero and came up with 19.62 m/s but i know that's not right.

for ball b i know that Vi in the y direction is Visinθ and x direction is Vicosθ but I'm not positive how to apply this information. I think I may have to use my knowledge of vectors too but I'm not sure. for example i think I use V=square root of (Vix^2 + Viy^2)

 

[voko]

When a ball is thrown straight upward, there is a indeed a certain point where its speed is zero. But where is that?

 

[zim70094]

the max height

 

[Nathanael]

the max height

What must the two situations (straight up and 40° angle) have in common?

 

[zim70094]

the max height? I'm not sure.

 

[zim70094]

Would I have to cut t (2s) in half?

 

[Nathanael]

What determines how long an object is in the air?

 

[zim70094]

i'm not sure. gravity?

 

[Nathanael]

Good, what else?

If I throw a ball perfectly horizontally it doesn't stay in the air very long, does it?

Why is that?

 

[zim70094]

because gravity is acting in the direction toward the ground...

 

[Nathanael]

Ok but what makes it last longer when I throw it upwards?

How would you calculate the time the object is in the air?

 

[zim70094]

Having an initial velocity. Please stop trying to raise your post count and provide a reasonable solution. I'm just trying to refresh myself on the subject and this was a problem I wasn't positive about.

 

[zim70094]

I'm down for helping me get to the solution, but you are being ridiculous.

 

[Nathanael]

You're not positive about the problem, and that's WHY I'm trying to help you understand. (As opposed to giving you the full solution in a single post...)

They BOTH have an initial velocity. What is different about the initial velocities? The VERTICAL component...

The time in the air depends on gravity and the vertical component of the velocity... Therefore both the "straight up throw" and "40° throw" must have the same vertical component of velocity.



P.S.
I could care less about my post count, but thanks for trying to be rude...

 

[Nathanael]

I'm down for helping me get to the solution, but you are being ridiculous.

People understand things better when they discover it themself.

I could tell you right off the bat that they both need to have the same vertical component, but what's the point in telling you that if you don't understand why...

 

[zim70094]

so I can use the two equations to find the missing variables? what does that have to do with max height?

 

[Nathanael]

what does that have to do with max height?

It doesn't directly have to do with max height, (I probably shouldn't have quoted you on my first reply) but two objects have the same max height if and only if they have the same initial vertical velocity (assuming they're launched from the same height).

And two objects have the same time in the air if and only if they have the same max height (assuming same launch height and gravity and what not)

so I can use the two equations to find the missing variables?

I don't know what two equations you're talking about but I'm sure you have it right

 

[ehild]

Read the original text: Both balls return to their initial level in 2 seconds.
You need the final height. You do not need the maximum height.

The balls are thrown from the ground, from height zero. Using y for height, y_i=0. What is the final height y_f?

The first ball is thrown vertically up from the ground. Returning to the original level means Δy= 0 . Apply your second equation Δy=v_it +a/2 t². v_i is the initial (upward velocity), and g=-9.81 m/s². You can determine v_i from this condition.
The second ball is given both horizontal and vertical initial velocity components, and performs both horizontal and vertical motion. Vertically it is the same as if it was thrown by the vertical component of its initial velocity.

ehild