Determine Initial Velocity, Max Ht for Diver Proj. Motion HW

• TheShehanigan
In summary, The diver leaves the end of a five meter high diving board and strikes the water three meters beyond the end. His initial velocity, height, and velocity when entering the water can all be determined using the homework equations.
TheShehanigan

Homework Statement

A high diver leaves the end pf a 5.0-m high diving board and strikes the water 1.3s later, 3.0m beyond the end of the board. Determine his inicial velocity, his maximum height and the velocity with which he enters water. (Projectile Motion).

*See details at the end*

Homework Equations

y = yo + vot + 1/2gt^2

The Attempt at a Solution

I have worked on this exercise, and can fully answer it using the water as the origin with the y-axis pointing upward. However, I wanted to try it with the diver leaving the board as the origin with the y-axis pointing downward (thus making g positive) and it's not giving me the correct result. Once I clear y = yo + vot + 1/2gt^2 for vo, I obtain vo = (y - yo + 1/2gt^2)/t. Since I am using the y-axis downward, I am making y = 5.00m and g = 9.8 m/s^2. I left the +1/2 gt^2 0 upon clearing the formula for vo since the acceleration is always downward (thus positive always).

However, it's not giving me the right result. Someone see anything wrong with my logic?

*I don't need help with the problem per-se, but with why the y component of velocity isn't giving me the right number. *

The correct answer should be 2.5 i for the y component of vo.

When you choose down as positive y then the sense of velocity and acceleration are both changed. Picking a proper origin is also complicating.

It should all work out the same, but you will need to take care in what is y=0 and with +/- for Vyo as well as g.

So a = - g for upward becomes a = g for downward, (with g = 9.80 m/s^2) and what would be vo = + for upward becomes vo = - for downward, or what? Also, y = 0 is the exact last point of the diving board in the way I'm trying to make the exercise.

I uploaded a diagram for reference.

Attachments

• Diagram.JPG
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If Vo is against the direction you chose as positive, then of course it is negative.

What is the formula for determining initial velocity in projectile motion?

The formula for determining initial velocity in projectile motion is v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.

How do you find the maximum height for a projectile in motion?

The maximum height for a projectile in motion can be found using the formula h = (u^2sin^2θ)/2g, where h is the maximum height, u is the initial velocity, θ is the angle of projection, and g is the acceleration due to gravity.

What is the role of gravity in determining the initial velocity and maximum height of a projectile?

Gravity plays a crucial role in determining the initial velocity and maximum height of a projectile. It is the force that causes the projectile to accelerate towards the ground, and it affects the trajectory of the projectile. The acceleration due to gravity is also used in the formulas for determining initial velocity and maximum height.

How does air resistance affect the initial velocity and maximum height of a projectile?

Air resistance can decrease the initial velocity and maximum height of a projectile as it acts against the motion of the projectile. The force of air resistance increases as the velocity of the projectile increases, so it has a greater impact on high-velocity projectiles.

Can the initial velocity and maximum height of a projectile be determined without considering air resistance?

Yes, the initial velocity and maximum height of a projectile can be determined without considering air resistance. This is because air resistance only has a significant impact on projectiles with high velocities. For low-velocity projectiles, the effect of air resistance is negligible, and the calculations can be done without considering it.

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