# Physics: Projectile Motion with different starting and ending heights?

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In summary, the conversation discusses a physics problem involving a baseball player throwing a ball at a pole. The problem asks for the time it takes for the ball to travel 20 meters horizontally, the height of the ball when it reaches the pole, the final velocity of the ball, and the final angle of projection. The conversation also includes equations and suggestions for solving the problem.
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All the physics problems I have worked with thus far assume stating and ending at the same height. Any help is how to solve this is appreciated :-)

A baseball player throws a ball from height 1.5 meters at an angle of 30 degrees and an initial velocity of 20 m/s. He is trying to hit a pole 20 meters away which is 1.7 m tall. Forget about air drag, etc*how long does it take the ball to travel 20 meters (in the horizontal)
*what is the height of the ball when it reaches the pole?
*what is the final velocity of the ball?
*what is the final angle (assuming the ground is perfectly flat of course)

To find the time does this sound right?: t = (20meters)/(20m/s * cos (30))

This is where I am stuck... I would think height at 20 m is just the y component analyzed at 20 but I'm not sure about that. The final velocity I have not idea on and the final angle would probably be the sum of the x and y components although I don't know how to manipulate the formuli to get that :-( Any help is greatly appreciated :-)

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From any source can you find the equation of projectile motion which gives you the relation between x, y and angle of projection theta?

sure, do you mean y = (tan angle)x - ((gx^2)/(2(v(initial)cos(angle)^2) ?

x would be the distance to my object (in this case 20m)
I know the angle
I know acceleration due to gravity
The velocity I presume is the initial velocity before you break it into its components?

ok, find time taken to travel the 20m horizontaly using trig to find horizontal velocity
speed = distance/time ==> time = distance/speed
i would take 1.5m as being height=0 so the pole top is 0.2m then just add your 1.5 back in at the end, so esentualy your working out the change in height :]
now use trig again to find verticle velocity, you now know time to reach the pole.
use x=ut+(1/2)a(t^2) remember to keep track of your + and - signs
x=dissplacement, u=initial velocity(in this case vertical), a=acceleration, t=time

final velocity, horizontal doesn't change due to no horizontal forces hence obeys Newtons 1st law.
verticaly however use V^2=u^2+2ax
v=final velocity.
use c^2=a^2+b^2 (pythagoras) to combine ur horizontal and verticle components of the velocity.
also use trig with these velocity componetns to find the angle.
this is all true if the ball does reach the stick if the ball hits the floor befor it reaches the stick then your value for t will be incorect, if after working out your t like i stated you also use
v^2+u^2+2ax in the verticle to find the final verticle velocity (remember x is dissplacement not distance so here x would equal 1.5m) then use
v=u+at to find time. if this time is less than the time you calculated horizontaly then the ball won't reach the pole and use v=x/t ==> x=vt horizontal to see how far the ball travelsHope i helped.

## 1. What is projectile motion?

Projectile motion is the motion of an object through the air or space due to the force of gravity. It is a combination of horizontal and vertical motion, and the path of the object is a parabola.

## 2. How does the starting height affect projectile motion?

The starting height of a projectile will affect the initial vertical velocity of the object. If the object is launched from a higher starting height, it will have a greater initial vertical velocity and will take longer to reach the ground compared to an object launched from a lower starting height.

## 3. Does the ending height affect projectile motion?

Yes, the ending height can affect the final vertical velocity of the object. If the object is launched from a higher starting height and ends at a lower ending height, it will have a faster final vertical velocity compared to an object launched from a lower starting height and ending at a higher ending height.

## 4. How does air resistance affect projectile motion?

Air resistance can affect the horizontal and vertical components of projectile motion. It can slow down the horizontal velocity of the object, causing it to travel a shorter distance. It can also affect the vertical velocity of the object, causing it to take longer to reach the ground.

## 5. What is the relationship between starting and ending heights in projectile motion?

The relationship between starting and ending heights in projectile motion is dependent on the angle of launch. If the object is launched at an angle of 45 degrees, the starting and ending heights will be the same. However, if the angle of launch is different, the ending height will be higher or lower than the starting height.

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