150 kg Max and 120 kg Paul were on a 4-inch wide by 8-inch tall (10 cm x 20 cm)

Question

150 kg Max and 120 kg Paul were on a 4-inch wide by 8-inch tall (10 cm x 20 cm) four-meter long balance beam 1-1/2 meters above the ground. The beam's mass is 36 kg and its center of mass is at the center of the beam. Max is 2 meters from one end of the beam and Paul is one meter from the other end. When the police arrived, they claimed they were practicing the balance beam scene from "Swan Lake", but actually they were trapped on the beam by a pack of dogs.

C. If Max's bilious belly is 2-1/2 meters above the ground, and if Spot the dog hits Max square in the belly button at the top of his leap (when his vertical velocity is zero meters per second), and if the leap starts from the ground at a location one meter perpendicularly distant from the beam, what was Spot's leap velocity and angle?

Explanation / Answer

Here, u2sin2(theta)/2g = 2.5                 -------------------->   height of Spot's leap

Also,   u2 * sin(2theta)/2g = 1                 ---------------------->   horizontal distance of Spot's leap

Dividing these equation

=>    sin2(theta)/sin(2theta) = 2.5

=>    tan(theta)/2 = 2.5

=>     tan(theta) = 5

=> theta = 78.69   degree

=>    u2 * sin(157.38)/2g = 1

=> u = 7.138   m/sec

=>   Spot's leap velocity and angle = 7.138   m/sec    and    78.69   degree

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