Question

Standing on a balcony you throw your keys to a freind bellow. Once second after you release your keys, they have an instantanious velocity of 13.9 m/s, directed 45^o bellow the horizontal. What instantanious velocity did you give them ?

Note: I have the answer, but I need to know HOW to get the answer.

ANSWER: V_o= 9.83 m/s, theta= 0.11˚ below the horizontal

Answer 1

consider the motion in vertical direction :

V_oy = initial velocity = ?

V_fy = final velocity = 13.9 Sin45 = 9.83 m/s

a = acceleration = 9.8 m/s²

t = time = 1 sec

using the equation

V_fy = V_oy + a t

9.83 = V_oy + (9.8) (1)

V_oy = 0.03 m/s

consider the motion along X-direction

V_ox = initial velocity = ?

V_fx = final velocity = 13.9 Cos45 = 9.83 m/s

a = acceleration = 0 m/s²

t = time = 1 sec

using the equation

V_fx = V_ox + a t

9.83 = V_ox + (0) (1)

V_oy = 9.83 m/s

net initial velocity is given as

V_o = sqrt(V_ox² + V_oy²) = sqrt((9.83)² + (0.03)²) = 9.83 m/s

direction : = tan^-1(V_oy/V_ox) = tan^-1(0.03/9.83) = 0.11 degree