In Denver, children bring their old jack-o-lanterns to the top of a tower and co
ID: 1661897 • Letter: I
Question
In Denver, children bring their old jack-o-lanterns to the top of a tower and compete for accuracy in hitting a target on the ground. Suppose that the tower height is h = 10.00 m, and that the bulls-eye's horizontal distance is d = 3.5 m from the launch point. (Neglect air resistance.) f a jack-o-lantern is given an initial horizontal speed of 3.3 m/s, what are the direction and magnitude of its velocity at the following moments in time? (Let the +x axis point to the right.) (a) 0.75 s after launch (b) just before it lands
Explanation / Answer
A) Vx = 3.3 m/s
Vy = - gt = 9.8*0.75 = - 7.35 m/s
Direction = arctan (7.35/3.3) = 65.8 degree below horizontal
Magnitude = sqrt ( 7.35^2 +3.3^2) = 8.057 m/s
B) Vy = - sqrt (2 gh) = - sqrt(2*9.8*10) = - 14 m/s
Direction = arctan (14/3.3) = 76.7 degree below horizontal
Magnitude = sqrt (14^2 +3.3^2) = 14.4 m/s