Question

A placekicker kicks a football upward at an angle of 20 degrees and a speed of 5.0 m/s. At what other angle will he have to kick a second ball with the same speed to reach the same distance downrange? Ignore air resistance!

30 degrees, 45 degrees, 60 degrees, or 70 degrees

**not sure how to solve! thanks! :)

Answer 1

OK - first you need to find out how long th eball is in their for th efirst kick

Answer 2

Veritically the initial speed is 5 sin 20

and the time is given by

v=u+at

v=0 at peak height and a = g

this gives the time to peak: total time is double that time

Answer 3

please you have to use the formula for the range, namely
\[range=\frac{ v _{0}^{2} }{ g }\sin (2 \alpha)\]
where g is the gravity, v_0 is the initial speed and alpha is tha angle of launch.
So please calculate the range for your first football

Answer 4

ah okay
wait so what am i plugging in?

Answer 5

you have to use the formula above, and please insert your numerical data, namely:
Alpha=20, v_0=5, and g=9.81

Answer 6

oh okay so i get 5^2/9.81*sin(2*20)=1.89886?

Answer 7

I got 1.639

Answer 8

ohh okay! so what happens from there?

Answer 9

Now in order to find your answer you have to solve this equation:
\[\frac{ 5^{2} }{ 9.81 }\sin (2 x)=1.639\]
please try to solve that equation for x

Answer 10

okay:)

so i get to here, is this correct?
sin(2x)=0.643 ?

Answer 11

ok!

Answer 12

and then i forget how to isolate the x here:(

Answer 13

you have to to this:
\[x=\frac{ 1 }{ 2 }\sin^{-1} (0.643)\]

Answer 14

ohh okay:) and then now solve and get 0.349?

Answer 15

please you shoul get x=20

Answer 16

oh! yes sorry, my calc was in radian mode! fixed it:) what happens from here now?

Answer 17

please note that, I cna write this:
\[1.639=\frac{ 25 }{ 9.81 }2*\sin 20 \cos 20\]
do you agree?

Answer 18

oops... I can write...

Answer 19

it is the formula we have already used

Answer 20

okay:)

Answer 21

now, please note that:
\[\cos 20=\cos(90-70)=\cos 90 \cos 70-\sin 90 \sin 70= \sin 70\]
and:
\[\sin 20=\sin (90-70)=\sin 90 \cos 70-\cos 90 \sin 70=\cos 70\]
so, substituting into the formula for range, we have:
\[range=\frac{ 25 }{ 9.81 }*2 \sin 20 \cos 20=\]
\[=\frac{ 25 }{ 9.81 }2*\cos 70 *\sin 70=\frac{ 25 }{ 9.81 }*2 \sin 70 \cos 70\]
so other angle is 70°

Answer 22

ahh okay:) thank you @Michele_Laino :)

Answer 23

thank you!! :) @iheartfood

Answer 24

:)