- #1

Theia

- 122

- 1

- \(\displaystyle v_0\) is speed at time \(\displaystyle t = 0\),
- \(\displaystyle \alpha _0\) is the angle between positive \(\displaystyle x\)-axis and initial velocity vector (\(\displaystyle \alpha _0 \in (0, \pi/2)\)),
- \(\displaystyle t\) time in seconds,
- \(\displaystyle y_0 >0\) the \(\displaystyle y\) coordinate at time \(\displaystyle t=0\),
- \(\displaystyle g\) acceleration due the gravity.

Let \(\displaystyle T\) be the time when the projectile hits positive \(\displaystyle x\)-axis (i.e. the ground). Find the maximum horizontal displacement of the projectile and show that angle between initial velocity vector and velocity vector at time \(\displaystyle T\) is \(\displaystyle \pi/2\).