Evaluating a QB's Claim: Speed of Throw Required

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In summary, a quarterback claims to be able to throw a football a horizontal distance of 169.1 m at an angle of 30° above the horizontal. To verify this claim, the speed at which the quarterback must throw the ball is calculated using kinematics equations. After solving for the maximum height and time of flight, the equation R=\frac{v^2 sin2\theta}{g} is used to calculate the horizontal range. The resulting velocity is found to be 43.74 m/s. This equation is derived by splitting the motion into horizontal and vertical components.
  • #1
gmunoz18
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On this problem i have gotten stuck and i am not really sure why.

Homework Statement



A quarterback claims that he can throw the football a horizontal distance of 169.1 m (185 yd). Furthermore, he claims that he can do this by launching the ball at the relatively low angle of 30° above the horizontal. To evaluate his claim, determine the speed with which this quarterback must throw the ball. Assume that the ball is launched and caught at the same vertical level and that air resistance can be ignored.

Homework Equations



kinematics equations

The Attempt at a Solution



First I cut the trajectory in half to find the footballs maximum height

than on the y coordinate is at its vertex its velocity at that point is 0 so i was able to put that in as well

So my list came out as is

X coordinate Y coordinate
X=84.55 Y=48.814
Xi=0 Yi=0
a=0 a=-9.8 m/s/s
Vi=? Vi=?
V=? V=0

than in order to get more information i solved for the ball to hit the ground from its highest altitude i.e. 48.814 meters.

dist = 1/2 g t^2 (g=9.8 m/s/s) so i used this equation and came up with 3.1562 seconds

Now I was able to solve for Vi for Y coordinate which i got 30.93m/s

after this i just used the sin(30)=30.93/x and i got 61.8628m/s


Was there an easier way to do this problem am i missing something very simple? but this answer is not matching up and can't seem to get it

thanks i advance
 
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  • #2
sorry about the double post!
 
  • #3
This way may be a little easier, and I got an answer that works.

Just use the kinematic equation:

[tex]\Delta s = v_i t + \frac{1}{2} a t^2[/tex]

for each direction x and y. For each velocity, separate [tex]v_i[/tex] into components. Then you have two equations with two unknowns, so you can then solve for each unknown.
 
  • #4
would i use the seconds that i solved for t?
 
  • #5
gmunoz18 said:
would i use the seconds that i solved for t?

No. You're basically starting over with t as an unknown.

I did the problem myself this way. It's not too bad and really shouldn't take too long, I don't think as long as finding the height then the time the way you did.

To get you started a bit, write down the variables you already know, x, y, a.

Your unknowns are v and t. But you do know how to split v into [tex]v_1x[/tex] and [tex]v_1y[/tex]. So, then you should be able to solve for both t and v.
 
  • #6
ohh wow that is a lot easier thanks for the help
 
  • #7
Its a good practice to go the basic way--splitting the motion into horizontal and vertical, but this question can also be solved by using this formula for horizontal range. Isn't it faster to put in the values and get the result ?

[tex] R=\frac{v^2 sin2\theta}{g}[/tex]
 
  • #8
Google_Spider said:
Its a good practice to go the basic way--splitting the motion into horizontal and vertical, but this question can also be solved by using this formula for horizontal range. Isn't it faster to put in the values and get the result ?

[tex] R=\frac{v^2 sin2\theta}{g}[/tex]

I have not encountered this equation yet but when i used it i did not get the correct answer. this is as R as the entire range correct?
 
  • #9
I am pretty much confident that this equation is correct. and yes, R is the complete horizontal range, which, according to your question is 169.1 m

I got v=43.74 m/s.

maybe I'm wrong..:redface:
 
  • #10
Google_Spider said:
I am pretty much confident that this equation is correct. and yes, R is the complete horizontal range, which, according to your question is 169.1 m

I got v=43.74 m/s.

maybe I'm wrong..:redface:

No, that's the answer I got doing it the other way, but I'm not familiar with that equation either.
 
  • #11
chocokat said:
No, that's the answer I got doing it the other way, but I'm not familiar with that equation either.

Maybe you'll encounter these equations later. They are all over in books on projectile motion.
My teacher derived these equation for us, by splitting the motion into horizontal and vertical components.
Its like this :

Time of flight=[tex] \frac{2vsin\theta}{g}[/tex]

Range= [tex] \frac{v^2 sin2\theta}{g}[/tex]

Max height=[tex]\frac{v^2 sin\theta}{2g}[/tex]
 
  • #12
Google_Spider said:
I am pretty much confident that this equation is correct. and yes, R is the complete horizontal range, which, according to your question is 169.1 m

I got v=43.74 m/s.

maybe I'm wrong..:redface:

thats what i got i did it with only half the distance at first ha but when i did it for the full 169.1 it was perfect!

Thanks a lot googlespider and chococat you helped alot!

What physics are you in google_spider? general, calc based?
 

Related to Evaluating a QB's Claim: Speed of Throw Required

1. How is the speed of a QB's throw measured?

The speed of a QB's throw is typically measured using a radar gun or a specialized sensor technology. These devices capture the velocity of the ball as it leaves the QB's hand and can provide an accurate measurement of the speed of the throw.

2. What is considered a fast throw for a QB?

The average speed of a QB's throw is around 50-60 miles per hour. However, a fast throw can vary depending on factors such as the distance of the pass, the type of throw (e.g. short vs. long), and the QB's physical capabilities. In general, a throw with a speed of 65 miles per hour or higher is considered fast.

3. How important is a QB's throwing speed?

A QB's throwing speed is an important factor in their overall performance, but it is not the only determining factor. Other skills such as accuracy, decision-making, and reading defenses are also crucial for a QB's success. However, having a fast throwing speed can give a QB an advantage in certain situations, such as making quick and difficult throws under pressure.

4. Can a QB's throwing speed be improved?

Yes, a QB's throwing speed can be improved through proper training and technique. Strength and conditioning exercises, along with proper throwing mechanics, can help a QB increase their throwing speed over time. However, it is important to note that a QB's natural physical abilities also play a significant role in their throwing speed.

5. Is a higher throwing speed always better for a QB?

Not necessarily. While a fast throwing speed can be advantageous, it is not always the most important factor in a QB's success. A QB must also have the ability to throw with accuracy, make good decisions, and adapt to different game situations. In some cases, a QB with a slightly slower throwing speed but better overall skills may outperform a QB with a higher throwing speed.

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