Standing on a balcony, you throw your keys to a friend standing on the ground below. 1.2 seconds after you release the keys, they have an instantaneous velocity of 15.4 m/s, directed 60° below the horizontal. What initial velocity did you give them?

Answer 1

15.4@-60=horizontal@0+vertical^-90+g*1.2@-90

ok, then
[email protected]@-90=Horizontal@0-(vertical+1.2g)@-90

setting components equal

15.4sin60=vertical+1.2*9.81 solve for the initial vertical component down.

15.4 cos60=horizontal
now you have the initial horizontal and vertical components, solve for initial velocity

intialvelocity=sqrt(hor^2+vert^2)@arctan vertical/horizontal downward.