Trajectory of diver with vertical and horizontal velocities

In summary, the problem involves a high diver jumping off a 5 m diving board and landing 1.3s later in the water 3 m beyond the end of the board. Using the equations for velocity and position, the initial velocity, maximum height reached, and velocity upon entering the water can be determined. The final answer can be expressed in Cartesian or polar coordinates. The Pythagorean theorem is used to find the magnitude of the velocity vector.
  • #1
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Please help me with this problem! :confused: I can't seem to get it set up quite right.
A high diver leaves the end of a 5 m high diving board and strikes the water 1.3s later 3 m beyond the end of the board. Considering the diver as a particle,d etermine a) her initial velocity, B. the maximum height reached and c. the velocity withwhich she enters the water.
I tried using these formulas: Vx = Vx0, x=x0+Vx0t
Vy = Vy0-gt, y = y0 + Vy0t- .5gt^2, v^2y = V^2y0 -2g(y-y0)
 
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  • #2
Hint: In this case movement in x-direction and in y-direction are independent.

Initial position (x0, y0) is given, vx0 is easy to compute, vy0 also computable. Knowing x0,y0,vx0,vy0 and the movement equation is sufficient to calculate the whole path. The formulas you present above are sufficient to solve the problem (still trying to find out what the last one is supposed to be - it can´t be correct just from looking at the units).
 
  • #3
Since the info provided only gave positions, I used the equation for position rather than velocity.

[tex]s_f=s_i+vt+\frac{1}{2}at^2[/tex]
Solve for v (velocity)

Hint: You use the water as your frame of reference, making your final position 0. Acceleration due to gravity is downward, or negative.

That gives you your initial vertical velocity (or along the y-axis). Your horizontal velocity is just the change in horizontal position divided by time.

You can express your final answer in Cartesian coordinates (your horizontal velocity, vertical velocity) or polar coordinates (magnitude of the velocity vector, angle of trajectory). The magnitude of the vector is found by plugging the x-axis and y-axis velocities into the Pythagorean theorem.
 
  • #4
I think I get it now. Thanks
 

Related to Trajectory of diver with vertical and horizontal velocities

1. How does the vertical velocity affect the trajectory of a diver?

The vertical velocity of a diver affects the height and speed of their dive. A higher vertical velocity will result in a higher jump and a faster descent, while a lower vertical velocity will result in a lower jump and a slower descent.

2. What is the role of horizontal velocity in a diver's trajectory?

The horizontal velocity of a diver determines the distance they will travel from their starting point. The higher the horizontal velocity, the further the diver will travel horizontally before reaching the water.

3. How are the vertical and horizontal velocities related in a diver's trajectory?

The vertical and horizontal velocities are independent of each other and do not affect each other. This means that a diver can have a high vertical velocity and a low horizontal velocity, or vice versa.

4. Can the trajectory of a diver be predicted accurately?

Yes, the trajectory of a diver can be predicted accurately using mathematical equations and taking into account the diver's initial vertical and horizontal velocities, as well as factors such as air resistance and gravity.

5. What factors can affect the trajectory of a diver?

The trajectory of a diver can be affected by various factors such as the diver's initial vertical and horizontal velocities, air resistance, gravity, wind speed and direction, and the angle at which the diver enters the water.

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