Chapter 2: Q. 65 (page 63)

One game at the amusement park has you push a puck up a long, frictionless ramp. You win a stuffed animal if the puck, at its highest point, comes to within 10 cm of the end of the ramp without going off. You give the puck a push, releasing it with a speed of 5.0 m/s when it is 8.5 m from the end of the ramp. The puck’s speed after traveling 3.0 m is 4.0 m/s. How far is it from the end when it stops?

Short Answer

Expert verified

The puck stops just before the winning distance. Therefore, you do not win the game.

Step by step solution

Step 1. Write the given information

the initial speed of the puck is $v_{i} = 5 m / s e c$

The distance of the puck from the end of the ramp is $x_{i} = 8.5 m$

The final speed of the puck is localid="1648461347758">vf=4m/sec

The distance at this point is $x_{f} = 3 m$

Step 2. To determine the position of the puck from the end

The acceleration of the puck is represented by $a$

Using the equation of motion,

${(v_{f})}^{2} - {(v_{i})}^{2} = 2 a S$

Here, the distance is given by role="math" localid="1648461855316" $S = 3 m$
Substitute the known values,

$4^{2} - 5^{2} = 2 (a) (3) 16 - 25 = 6 a a = - 1.5 m / s^{2}$

This is the acceleration of the puck when it has traveled a 3 m distance.

Now, to determine the distance at which it stops
write the equation of motion,

$v^{2} - {v_{i}}^{2} = 2 a s 0 - 5^{2} = 2 (- 1.5) s s = \frac{25}{3} s = 8.33 m$
The puck stops just before the winning distance. Therefore, you do not win the game.

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Short Answer

Step by step solution

Step 1. Write the given information

Step 2. To determine the position of the puck from the end

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