Projectile Motion ball throw help

In summary, the problem involves a ball being thrown off a cliff at an angle of 30 degrees above the horizontal and striking the ground 10.4 seconds later. The goal is to determine the initial velocity of the ball, the maximum height it reaches, and its final impact velocity. The solution involves dividing the problem into two sections, using kinematic equations, and solving for the initial velocity.
  • #1
d21
1
0

Homework Statement


A ball is thrown off of a 15m cliff at an angle of 30 degrees above the horizontal and strike the ground 10.4 seconds later. Determine the initial velocity of the ball, the maximum height of the ball, and impact (final) velocity of the ball.

Homework Equations


vo=vf+at
y=.5at+vot
x=vot

The Attempt at a Solution


I'm really out of my depth on this problem. I really just have no clue where to begin, since I'm used to being given the initial velocity of the ball. I had an idea to try to divide up the time of the problem into two sectors, where the ball is in its parabolic motion in one section and the other where it comes back to the same level that it was launched at and continues to the ground. the time would be √2h/g correct? But can I use this even though there's a y component to the velocity? Is any of this even correct? How do I do this problem?

Or can I just say y=.5gt^2+vot
-15=.5(-10)(10.4)^2+vo(10.4)?
Vo=53.44?

Also isn't this just the vertical component of Vo? So shouldn't the full Vo be
Voy=VoSin30
53.44=VoSin30
Vo=106.88?
 
Last edited:
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  • #2
well, you do have to work in sections. when the ball comes back to the same level on the other side, it has the same magnitude of vertical velocity (the direction is opposite) it had at launch time. from here on, you know the height to the bottom, calculate final vertical velocity.
Use the equation
V^2 - Vo^2 =2as

it should become simple from here on.
 
  • #3
NahilSh said:
you do have to work in sections.
That would be if you were using the standard ballistics equations.
Alternately - draw a v-t diagram for horizontal and vertical components of the motion.
Or just applying the kinematic equations, as d21 has done.

d21 said:
I'm used to being given the initial velocity of the ball.
Welcome to PF;
Proceed as you normally would, just leave the initial velocity as a variable.
You'll end up with a system of simultaneous equations which you can solve for the initial speed.

As NahilSH said, you can finess the process by realising that the speed is the same at the initial height but coming down.
 
  • #4
Simon Bridge said:
That would be if you were using the standard ballistics equations.
Alternately - draw a v-t diagram for horizontal and vertical components of the motion.
Or just applying the kinematic equations, as d21 has done.

yeah, true...:redface: but it does help to work in sections to simplify the process.
 
  • #5
It can help to break the process into stages, and solve each stage in turn. Yep.
 

1. What is projectile motion?

Projectile motion is the motion of an object through the air, under the influence of gravity, after being launched or thrown.

2. What factors affect projectile motion?

The factors that affect projectile motion include the initial velocity, angle of launch, mass of the object, and the effects of air resistance and gravity.

3. How does the angle of launch affect the trajectory of the projectile?

The angle of launch affects the trajectory of the projectile by determining the vertical and horizontal components of its initial velocity. The greater the angle, the higher the vertical velocity, resulting in a higher peak height and longer flight time. A lower angle will result in a shorter flight time and less vertical displacement.

4. How does air resistance impact projectile motion?

Air resistance, also known as drag, can reduce the horizontal distance and increase the time of flight of a projectile. This is because air resistance acts in the opposite direction of the projectile's motion, slowing it down and reducing its range.

5. Can projectile motion be used to calculate the distance and velocity of a thrown object?

Yes, projectile motion equations can be used to calculate the distance and velocity of a thrown object, as long as the initial conditions and other factors are known. This can be useful in a variety of fields, such as sports, engineering, and physics.

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