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

AI Thread Summary
To determine the maximum width of a river that can be crossed with an initial velocity of 30 m/s, the initial velocity must be split into horizontal and vertical components using trigonometric functions. The vertical motion equation, y = v_y * t - 0.5 * g * t^2, is used to find the time of flight, where y equals zero when the ball lands. The horizontal distance, or river width, is calculated using the range formula R = v_x * t, where v_x is the horizontal component of the initial velocity. Understanding both components is crucial for solving the problem effectively. The discussion emphasizes the need for a step-by-step approach to clarify the relationship between time and distance in projectile motion.
stressedgirl
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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?
 
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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=vyt_0.5gt2 to get the time for this motion.

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

that 't' in the equation for 'R' is the time for the motion above.
 
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
 
stressedgirl said:
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.
 
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
 
stressedgirl said:
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=vyt-0.5gt2

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

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