Physx141MPch6sol

Physx141MPch6sol - 6.2 Model The boat is treated as a particle whose motion is governed by constant-acceleration kinematic equations in a plane

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6.2. Model: The boat is treated as a particle whose motion is governed by constant-acceleration kinematic equations in a plane. Visualize: Solve: Resolving the acceleration into its x and y components, we obtain () ( ) 22 ˆˆ 0.80 m/s cos40 0.80 m/s sin40 ai + r j ° ( ) ( ) 0.613 m/s 0.514 m/s ij =+ From the velocity equation , 10 vva tt rrr ( ) ( ) 1 ˆ 5.0 m/s 0.613 m/s 0.514 m/s 6 s 0 s vi i j  +  r ( ) ( ) 8.68 m/s 3.09 m/s r The magnitude and direction of are v 8.68 m/s 3.09 m/s 9.21 m/s v =+= 1 11 1 3.09 m/s tan tan 20 8.68 m/s y x v v θ −−  ==   = ° north of east Assess: An increase of speed from 5.0 m/s to 9.21 m/s is reasonable. 6.6. Model: The model rocket will be treated as a particle. Kinematic equations in two dimensions apply. Air resistance is neglected. Visualize: The horizontal velocity of the rocket is equal to the speed of the car, which is 3.0 m/s. Solve: For the rocket, Newton’s second law along the y-direction is: net R R FFm g m a =−= rr ( ) 2 1 8.0 N 0.5 kg 9.8 m/s 0.5 kg y a ⇒= 2 6.2 m/s = Thus using 2 1 10 010 2 yy yy v tt a − + , 2 2 1 1R 2 20 m 0 m 0 m 6.2 m/s 0 s t =++ ( ) ( ) 1 20 m 3.1 m/s t 1 2.54 s t Since t 1 is also the time for the rocket to move horizontally up to the hoop,
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() 2 1 10 010 1 0 2 xx x xvt t a t t =+ −+ ( )( ) 0 m 3.0 m/s 2.54 s 0 s 0 m = 7.62 m Assess: In view of the rocket’s horizontal speed of 3.0 m/s and its vertical thrust of 8.0 N, the above-obtained value for the horizontal distance is reasonable. 6.11. Model: The bullet is treated as a particle and the effect of air resistance on the motion of the bullet is neglected. Visualize: Solve: (a) Using ( 2 1 100 10 2 yy yyvtt a tt − + ) , we obtain ( ) 2 22 1 1 2 2.0 10 m 0 m 0 m 9.8 m/s 0 s t −× = + +− 1 0.0639 s t ⇒= (b) Using 2 1 1 0 2 x xvtt a , ( ) 0 50 m 0 m 0.0639 s 0 s 0 m x v 0 782 m/s x v Assess: The bullet falls 2 cm during a horizontal displacement of 50 m. This implies a large initial velocity, and a value of 782 m/s is understandable.
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This note was uploaded on 05/05/2008 for the course PHYS 141 taught by Professor Staff during the Spring '06 term at Cal Poly.

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Physx141MPch6sol - 6.2 Model The boat is treated as a particle whose motion is governed by constant-acceleration kinematic equations in a plane

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