Football, time in air/distance

[Neliel06]

Homework Statement

To get the maximum range, a football kicker kicks a football (at ground level) at an angle of 45degrees. The initial speed of the football is 20 m/s.

a. How long is the football in the air?
b. How far up-field does the football hit the ground?

Homework Equations

The Attempt at a Solution

Well originally i thought, i must use X=Xo+1/2(V+Vo)t
to get the time, but that requires X, which is also asked for and not given.
So then i tried getting X. So i used Rmax= Vo^2/g
20/9.8=40.8m
And i also needed V. so i used V^2=V0^2+2a(X-X0)
and got V=34.6 m/s

I plugged those in as X and V and got time=1.5 seconds

However, i only got partial credit, so i don't know where i went wrong

 

[rl.bhat]

Time of flight = 2V_0*sin(theta)/g

 

[thomate1]

.

I would like to clarify that there are a few assumptions made in this problem. First, it assumes that air resistance is negligible and that the football is kicked on a level surface. Additionally, it does not specify the mass of the football, which could affect the calculations.

To answer the first question, we can use the equation t = 2Vsinθ/g, where V is the initial velocity (20 m/s) and θ is the angle of the kick (45 degrees). Plugging in these values, we get t = 1.4 seconds.

For the second question, we can use the equation R = V^2sin2θ/g, where R is the range of the football. Plugging in the same values as before, we get R = 40.8 meters.

It is possible that the incorrect answer was due to a rounding error or an incorrect application of the equations. It is important to double check all calculations and make sure the correct units are used. Additionally, it would be helpful to provide a clear explanation of the steps taken to solve the problem.