Question

you toss your keys at the desk. keys leave your hand at y0 = 2.04 meters above the floor traveling at an angle 𝜃 = 11.7 degrees above the horizontal. The keys land exactly in the middle of the desk (ydesk = 0.85 meters high and xdesk = 4.64 meters away).
a)initial velocity of the keys?
b)time they were in the air for?

Answer 1

Hi = initial height above desk = 2.04-0.85 = 1.15
Vi = initial velocity magnitude
u = constant x velocity = Vi cos 11.7
T = time in air = 4.64/u = 4.64 / Vicos11.7
so when at desk
0 = 1.15 + Vi sin 11.7 T - 4.9 T^2
0 = 1.15 + Vi sin (11.7)[ 4.64/Vicos11.7] - 4.9 [4.64/Vicos11.7]^2
solve for Vi and go back for T etc