In Denver, children bring their old jack-o-lanterns to the top of a tower and co

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 (Figure 4-17). Suppose that the tower height is h = 8.60 m, and that the bulls-eye's horizontal distance is d = 4.1 m from the launch point. (Neglect air resistance.)

If 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
    

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 (Figure 4-17). Suppose that the tower height is h = 8.60 m, and that the bulls-eye's horizontal distance is d = 4.1 m from the launch point. (Neglect air resistance.)

Explanation / Answer

a) vx = 3.3

vy = 9.81*0.75=7.36

mag = sqrt(3.3^2 + 7.36^2)=8.07 m/s

angle = arctan(vy/vx) = arctan(7.36/3.3)=65.85 degrees

b) just before it hits we need to find vy

vy^2 = v0y^2 + 2 ay
vy = sqrt( 3.3^2 + 2*9.81*8.6)=13.4 m/s

v =sqrt(13.4^2 + 3.3^2)=13.8 m/s

angle = arctan(vy/vx) = arctan(13.4/3.3)=76.17 degrees

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