Calculating Maximum River Crossing Distance with Initial Velocity of 30 m/s

[stressedgirl]

Homework Statement

If you can hurl a ball so that its initial speed is 30 m/s, what is the widest river it can cross?

v1 = 30m/s

Homework Equations

I am not sure with only the one variable given.

The Attempt at a Solution

Start with a x and y component diagram?

 

[rock.freak667]

Yes split the inital velocity into vertical and horizontal components.

Now consider vertical motion, when the ball lands on the ground again, the displacement is zero. Use y=v_yt_0.5gt² to get the time for this motion.

Now horizontally the Range (how wide your river is) is given by R=v_xt

that 't' in the equation for 'R' is the time for the motion above.

 

[stressedgirl]

Umm.. I don't understand. How would the 't' answer the question? Wouldn't I need a 'd' since it's asking how wide the river could be?

edit: SOrry I don't really understand what I'm even supposed to draw in the diagrams of the components

 

[rock.freak667]

Umm.. I don't understand. How would the 't' answer the question? Wouldn't I need a 'd' since it's asking how wide the river could be?

edit: SOrry I don't really understand what I'm even supposed to draw in the diagrams of the components

Solving for the 't' would get the 'd'.

Draw the 30m/s at an angle θ and split it into vertical and horizontal components.

 

[stressedgirl]

Can I get something step by step please? I drew the components but I don't get why I even have to have both an x and the y. I just have two sets of axes and a theta angle at 90degrees

 

[rock.freak667]

Can I get something step by step please? I drew the components but I don't get why I even have to have both an x and the y. I just have two sets of axes and a theta angle at 90degrees

You will see why you need it soon.

Did you get your components as

y: 30sinθ

x: 30 cosθ

These are your initial velocity components

Now consider vertical motion: y=v_yt-0.5gt²

When the ball hits the other side of the river, y = 0. So solve for 't' and tell me what you get.