Solving a QB's Claim: Determining Speed of a Football Throw

[gmunoz18]

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 in advance

 

[G01]

Can you show how you found the maximum height of the ball?

 

[Moetasim]

As a scientist, it is important to always critically evaluate our methods and results. In this case, it seems like you have followed the correct steps in solving the problem, but there may be some errors in your calculations or assumptions. It would be helpful to double check your calculations and make sure you are using the correct equations and values.

Additionally, it is always a good idea to consider different approaches to a problem. In this case, you could also use the equation v^2 = v0^2 + 2ad to solve for the initial velocity (vi), where v is the final velocity (in this case, the horizontal velocity of the ball), v0 is the initial velocity (which is 0), a is the acceleration (which is the horizontal acceleration of the ball), and d is the distance (which is 169.1 m). This may provide a simpler and more direct approach to solving for the initial velocity.

Overall, it is important to always double check our work and consider alternative methods to ensure accuracy in scientific problem solving.