Solve 2D Motion Problem: Ball Hitting Canyon Edge

In summary, the problem involves finding the coordinates where a ball with a velocity of 10m/s hits a canyon with the equation y^2=16x. After converting the ball's motion into a function of x for y and setting it equal to y=Sqrt(16x), the individual was unable to solve the equation. However, the book suggests that plotting the two curves of y=4*Sqrt[x] and y=-4*Sqrt[x] can help determine which one resembles a canyon. The individual realizes their mistake and thanks the other person for their help.
  • #1
mewmew
114
0
Ok, in this problem a ball with velocity 10m/s flys off the horizontal edge of a canyon, the equation for the canyon is y^2=16x and it wants you to find the x,y cordinates where the ball hits it. I turned the balls motion into a a function of x for y and then set that equal to y=Sqrt(16x) but I can't solve it. It is an easy problem the book says but I can't do the math, or perhaps its my method, to figure it out. Thanks a lot for any help.
 
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  • #2
If you solve y^2=16x for y, you get y=4*Sqrt[x] and y=-4*Sqrt[x].

Plot the two curves and decide for yourself which one looks like a canyon. I think you should be able to solve it then.
 
  • #3
Thanks, I am really dumb and was doing my equations wrong :)
 
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FAQ: Solve 2D Motion Problem: Ball Hitting Canyon Edge

1. How do you calculate the initial velocity of the ball?

The initial velocity of the ball can be calculated using the formula V = d/t, where V is the velocity, d is the distance traveled, and t is the time taken.

2. What factors affect the motion of the ball?

The motion of the ball is affected by factors such as gravity, air resistance, the angle at which the ball is launched, and the initial velocity of the ball.

3. How do you determine the maximum height reached by the ball?

The maximum height reached by the ball can be determined using the formula h = (V^2 * sin^2θ)/(2g), where h is the maximum height, V is the initial velocity, θ is the angle of launch, and g is the acceleration due to gravity.

4. What is the equation for calculating the range of the ball?

The range of the ball can be calculated using the formula R = (V^2 * sin2θ)/g, where R is the range, V is the initial velocity, θ is the angle of launch, and g is the acceleration due to gravity.

5. How can you determine the time of flight for the ball?

The time of flight for the ball can be determined using the formula t = 2Vsinθ/g, where t is the time of flight, V is the initial velocity, θ is the angle of launch, and g is the acceleration due to gravity.

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