How Do You Solve Projectile Motion Problems Involving Non-Zero Final Heights?

[jonw39]

A field goal kicker kicks the football so that it leaves the ground with velocity V that is 50 degrees above horizontal. The ball travels for 3.24s and hits the crossbar 10.00 ft above the ground. Neglect air resistance.
Find the velocity after the kicker kicks the ball.
Find the horizontal distance the ball was from when kicked.
Ok, I wrote all the basic equations of motion. All my attempts to combine the equations through substitution netted me too many variables and I couldn't solve anything. I really don't understand where I'm going astray. This problem wouldn't be very difficult if the ball wasn't hitting the crossbar above the ground. Also, finding the distance would by child's play if I could just wrangle the initial velocity out of this thing.

Edit: This isn't really a homework problem, it's on a study guide and I'm almost certain I'll see something like it on my exam tomorrow. I'm not looking so much for a solution but a general strategy that let's me attack projectile problems like this when the projectile doesn't land at y=0.

 

[ThalorB]

Having too many variables is likely the point of the exercise. Have you tried picking some approximate values for the initial velocity to find the range wherein it lies? A spreadsheet makes this a relatively simple task.

 

[jonw39]

Having too many variables is likely the point of the exercise. Have you tried picking some approximate values for the initial velocity to find the range wherein it lies? A spreadsheet makes this a relatively simple task.

I'm going to be expected to do this with just a scientific calculator. I know there is a simple way to figure this out that is just flying right over my head.

 

[PeterO]

A field goal kicker kicks the football so that it leaves the ground with velocity V that is 50 degrees above horizontal. The ball travels for 3.24s and hits the crossbar 10.00 ft above the ground. Neglect air resistance.
Find the velocity after the kicker kicks the ball.
Find the horizontal distance the ball was from when kicked.



Ok, I wrote all the basic equations of motion. All my attempts to combine the equations through substitution netted me too many variables and I couldn't solve anything. I really don't understand where I'm going astray. This problem wouldn't be very difficult if the ball wasn't hitting the crossbar above the ground. Also, finding the distance would by child's play if I could just wrangle the initial velocity out of this thing.

Edit: This isn't really a homework problem, it's on a study guide and I'm almost certain I'll see something like it on my exam tomorrow. I'm not looking so much for a solution but a general strategy that let's me attack projectile problems like this when the projectile doesn't land at y=0.

Firstly deal with the vertical component - we can convert to the actual velocity later.
First list the variables:
V_o = ? - I use the question marks as this is what we are after.
V_f
x = 10
t = 3.24
a = -9.8

we need the equation that has no V_f in it.

x = V_o.t + 0.5.a.t²

substitute

10 = V_o x 3.24 - 4.9 x 3.24²

re-arrange and solve for V_o
Remember this is just the vertical component, you have to undo some trig on the 50^o angle to find the actual velocity.

I reckon you should be able to do it from there.

 

[jonw39]

we need the equation that has no V_f in it.

x = V_o.t + 0.5.a.t²

substitute

10 = V_o x 3.24 - 4.9 x 3.24²

re-arrange and solve for V_o
Remember this is just the vertical component, you have to undo some trig on the 50^o angle to find the actual velocity.

I reckon you should be able to do it from there.

I don't agree. All that equation says is that in 3.24 seconds the ball travels up 10 ft from zero. What's happening is the ball is traveling up to a height y₂ then down to 10ft. Were also in ft here so it's easier to use ft/s² for the acceleration.

Anyway my exam is in 5 minutes so, hopefully I can figure it out if it shows up.

edit:Test done, went well, this didn't show up. Still interested in an answer.

 

[PeterO]

I don't agree. All that equation says is that in 3.24 seconds the ball travels up 10 ft from zero. What's happening is the ball is traveling up to a height y₂ then down to 10ft. Were also in ft here so it's easier to use ft/s² for the acceleration.

Anyway my exam is in 5 minutes so, hopefully I can figure it out if it shows up.

edit:Test done, went well, this didn't show up. Still interested in an answer.

The mistake I made was not converting the 10 ft to metres - we dropped feet etc in 1974.

The beauty of the motion formulas is that they include displacement - so all that is important is that the object [the ball] finishes its journey 10 ft [3.xxxxx m ] above where it started.

So I should have adjusted the height to metres, or perhaps used the ft equivalent of g - I recall it is about 32?

Once you have found the initial velocity, you could use that same formila, but use the V_o value and use just t to find when it was at height 10 ft and you will get not only 3.24 seconds, buta time much less that 1 second. That little time is on its way up.

 

[jonw39]

The mistake I made was not converting the 10 ft to metres - we dropped feet etc in 1974.

The beauty of the motion formulas is that they include displacement - so all that is important is that the object [the ball] finishes its journey 10 ft [3.xxxxx m ] above where it started.

So I should have adjusted the height to metres, or perhaps used the ft equivalent of g - I recall it is about 32?

Once you have found the initial velocity, you could use that same formila, but use the V_o value and use just t to find when it was at height 10 ft and you will get not only 3.24 seconds, buta time much less that 1 second. That little time is on its way up.

Oh wow, I didn't think the motion equations worked like that. Though, I guess being a second degree polynomial should have been a huge tip off.

Problem solved.