Two well-trained poodles, Toto and Pico, sit on the left and right ends of a ska
ID: 1410316 • Letter: T
Question
Two well-trained poodles, Toto and Pico, sit on the left and right ends of a skateboard, respectively. The skateboard is initially at rest on a horizontal surface, and you may assume that no energy is lost due to friction. The mass of the skateboard is 4.00 kg, Toto’s mass is 5.00 kg and Pico’s mass is 6.00 kg. When the trainer says “JUMP!” each dog instantly jumps. Toto jumps to the left at a speed of 3.00 m/s at a 35.0 angle above horizontal, and Pico jumps to the right at a speed of 2.00 m/s at a 60.0 angle above horizontal. Find the skateboard’s speed and direction after the two dogs jump off. The answer should be 1.57m/s to the right, please provide a complete solution together with diagrams. Thank you.
Explanation / Answer
We can apply the law of conservation of momentum.The initial momentum of the system was zero , because the system was at rest initially .
According to the conservation of the momentum the system must remain at zero momentum if no external force acts on it.
After the dogs jump off, equating the linear momentum along the x direction
mp vpx - mt vtx + M Vx = 0
Where the subscripts p and t denote pico and toto. The x components of the velocities are taken . The negative sign for the vtx is taken because toto jumps in the negative x direction
M and Vx denote the velocity of the board in the x direction
6 kg x (2 m/s) cos 60 - 5 kg x (3 m/s) cos35 = - (4 kg ) Vx
Vx = - (6 - 12.29) / 4
Vx = 1.572 m/s
We have taken the "right" direction as positive
Vx = 1.572 m/s towards the right
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