Projectile Motion - Rock Thrown Horizontally Off a Cliff

  1. 1. The problem statement, all variables and given/known data
    A student stands on the edge of a cliff and throws a stone horizontally over the edge with a speed "v1". The cliff is "h" meters high. Given [h,v1], Determine:
    a. The time to hit the ground
    b. The horizontal distance traveled
    c. The magnitude and direction of the stone's velocity just before hitting the ground

    2. Relevant equations
    x direction

    y direction

    3. The attempt at a solution
    If I set up my coordinate system so that 0 is ground level, and h is cliff level (where the stone was thrown from), and the distance to the landing point of the stone when it hits the ground is, say "r" meters from 0 in the x direction.

    I've shown what work I have in the attached images, but to be perfectly honest, I'm having trouble with the entire basic strategy to approaching this problem.

    When I try to solve for x distance r, I need time. So when I try to solve for time, that becomes reliant on r. I can't even think of anything else I can find.

    I feel I'm either not utilizing the possible angles within this problem, or I've completely missed some fundamental idea in regards to projectile motion.

    A good shove in the right direction on this kind of problem would be VERY much appreciated.

    Attached Files:

  2. jcsd
  3. Here's a simple approach:-

    Firstly make a table of Horizontal motion and vertical motion, like according to your question,

    H-Horizontal motion
    V-Vertical motion
    u-initial velocity
    h-Height of the cliff
    x and t are assumed since we have to find them out.

    Ok, first lets see in which column, assumed variable are less. Its obvious that in V column, there is only one variable "t". So can you apply equation of motion here? :smile:
  4. Something tells me I've once again forgotten a rather important fact about the equation

    Is it correctly written as this by chance :grumpy:
  5. You can take y0 as 0 since the initial displacement is zero. :smile:

    Now just plug in the values and you will get the time. :)
  6. How about this then:
  7. That's right. :smile:

    Now just see that we have t same for both H and V motion. So now we are left with x in H motion. Try applying the suitable equation of motion in the H column.
  8. Here is my attempt for Horizontal distance covered:
    hows that look?

    Now in order to get the direction and magnitude of the end velocity of the rock, I need both the Vx and Vy right?
  9. Yep, that's right. :smile:

    Now you have solved the first two parts. About the third part, you can go like this:-
    Find the final velocity in Horizontal and Vertical direction, then find their resultant. :)
  10. Alright, so far so good, lets see if I got this right:

    To find the Velocity in the y direction near point of impact

    substitute in my knowns:
    [tex]V_y = \sqrt{2gh}[/tex]

    As for the resultant, are you referring to vector addition?

    If so, I think I got [tex]<V_1,0,0>+<0,\sqrt{2gh},0>\ = \ <V_1,\sqrt{2gh},0>[/tex]

    Hows all of this look?

    But what if the question asked for the angle, would I need to use the Tangent Function and take the Inverse Tangent to find Theta?
  11. You got the final velocity right but with a long method. :smile:
    What i expected was that you would have used the first equation of motion.

    Yep, i am referring to vector addition. I think you did it by co-ordinates. I have never used that way. :smile:
    We have horizontal and vertical final velocities. These both are perpendicular to each other.
    So [tex]V=\sqrt{V_x^2+V_y^2}[/tex]

    V is the resultant velocity.

    Just plug in the values and your are done. :smile:

    If you want to find the angle, you need to first specify the reference, Horizontal or vertical. :)
  12. Well, it seems I got a grasp of the problem now, I think the only thing that messed me up in the beginning was the fact that I was applying one of the formulas wrong.

    Thanks for all the help, its much appreciated :smile:
  13. Your welcome!!:smile:
    And remember the table approach. Whenever you deal with projectiles, the best way is to make the table :smile:

    I forgot to welcome you. Welcome to the board. Hope you enjoy your stay here. :smile:
    Before wandering on the board, have a look at the rules. They may help you.
  14. Thanks for the advice

    Thanks again
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