A 15 kg dog jumps out of a 40 kg canoe. If the dog\'s velocity is 1.2 m/s, what

Question

A 15 kg dog jumps out of a 40 kg canoe. If the dog's velocity is 1.2 m/s, what is the velocity of the canoe? 7. An 800 kg cannon mounted on wheels fires a 10 kg cannonball at 80 m/s. At what velocity does the cannon recoil? What are the final kinetic energies of each? 8. Tarzan has a mass of 80 kg and is about to be attacked by a gang of Amazon warriors. Jane has a mass of 60 kg and swings on a vine to come to his rescue, starting at 2 m/s and 5 m above the ground. What is her velocity when she reaches Tarzan a ground level? What is their velocity after Jane grabs Tarzan? (Hint: This would be a perfectly inelastic collision.) Will they be able to swing to safety on a tree branch that is 1.7 m above the ground? 9. 10. What if the above scenario was repeated but with Tarzan saving Jane from a gang of paparazzi?

Explanation / Answer

7.

Vi = initial velocity of d-g-canoe combination = 0

m = mass of dog = 15 kg

M = mass of canoe = 40 kg

v = velocity of dog after jump = 1.2 m/s

V = velocity of canoe after jump = ?

Using conservation of momentum

(m + M) Vi = m v + M V

(15 + 40) (0) = (15) (1.2) + (40) V

V = - 0.45 m/s

ther negative sign indicates opposite direction

8.

Vi = initial velocity of cannon-ball combination = 0

m = mass of ball = 10 kg

M = mass of canon = 800 kg

v = velocity of ball after fire = 80 m/s

V = velocity of canon after fire= ?

Using conservation of momentum

(m + M) Vi = m v + M V

(800 + 10) (0) = (10) (80) + (800) V

V = - 1 m/s

ther negative sign indicates opposite direction

kinetic energy of ball = (0.5) m v2 = (0.5) (10) (80)2 = 32000 J

kinetic energy of cannon = (0.5) M V2 = (0.5) (800) (-1)2 = 400 J

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