Vector Calc Question

[Pablo1204]

Hello,

Could someone please help me find where I went wrong in this projectile motion question.

Question:
A ball is thrown at ground level from origin O with initial speed of 50m/s. There is a wall 100 m to the right of O which is 20 m tall. Find the smallest possible projection angle such that the ball passes over the building. Use g=9.8

I got that the position vector is

Then subbed in

Which resulted in the projection angle being equal to 23.40 degrees however the textbook got 23.33 degrees.

Thanks

[RuiAce]

I played around with technology for this. WolframAlpha seems to suggest that \(\theta \approx 23.398^\circ\), so your answer should be correct (with rounding). I then checked on Desmos, and with \(\theta \approx 23.33^\circ\) I found that the ball doesn't clear the wall either.

The working you had provided seemed correct to me.

[Pablo1204]

Alright thank you for the clarification