College Physics, Volume 1
College Physics, Volume 1
2nd Edition
ISBN: 9781133710271
Author: Giordano
Publisher: Cengage
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Chapter 4, Problem 20P

(a)

To determine

The maximum height reached by the rock.

(a)

Expert Solution
Check Mark

Answer to Problem 20P

The maximum height reached by the rock is 77.051 m

Explanation of Solution

Write the equation of motion.

  v2u2=2as        (I)

Here, v is the final velocity, u is the initial velocity, a is the acceleration, and s is the height.

Conclusion:

Substitute 0 for v, 0.6342 for u, -9.8m/s2 for a in expression (I)

    v2u2=2as06.342=2×(9.8)×ss=2.051m

Therefore the maximum height of the rock reach is 2.051m plus the height of the bridge,

  75+2.051 = 77.051 m

(b)

To determine

The time required by the rock to reach the maximum height.

(b)

Expert Solution
Check Mark

Answer to Problem 20P

The time required by the rock to reach the maximum height is 0.647sec

Explanation of Solution

Write the equation of motion.

  v=u+at        (I)

Here, v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time interval.

Conclusion:

Substitute 0 for v, 0.6342 for u, -9.8m/s2 for a in expression (I)

  0 = 6.349.8 tt = 0.647sec

The time required by the rock to reach the maximum height is 0.647sec

(c)

To determine

The place where the rock lands.

(c)

Expert Solution
Check Mark

Answer to Problem 20P

The place where the rock lands is 62.7m

Explanation of Solution

Write the equation of motion.

  s=ut+12at2        (I)

Here, u is the initial velocity, a is the acceleration, s is the height, and t is the time interval.

Conclusion:

Substitute 0 for u, 77.051 for u, -9.8m/s2 for a in expression (I)

  s=ut+12at277.051=0+0.5×9.8ktt2t=3.965s

Total time taken to reach ground is 3.965 +0.647 = 4.612 s

Therefore the total horizontal displacement is,

  xlands =v0xtlands         (II)

Substitute 15m/s for v0x, 4.61s for tlands in expression (II)

  xlands=(15m/s)(cos25°)(4.61s)=63 m

The place where the rock lands is 62.7m

(d)

To determine

The time at which the rock lands.

(d)

Expert Solution
Check Mark

Answer to Problem 20P

The time at which the rock lands is  4.612 s

Explanation of Solution

Write the equation of motion.

  s=ut+12at2        (I)

Here, u is the initial velocity, a is the acceleration, s is the height, and t is the time interval.

Conclusion:

Substitute 0 for u, 77.051 for u, -9.8m/s2 for a in expression (I)

  s=ut+12at277.051=0+0.5×9.8ktt2t=3.965s

Total time taken to reach ground is 3.965 +0.647 = 4.612 s

The time at which the rock lands is  4.612 s

(e)

To determine

The velocity of the rock just before it lands.

(e)

Expert Solution
Check Mark

Answer to Problem 20P

The magnitude of the velocity 41.167 m/s and 70.72°.

Explanation of Solution

Write the equation of motion.

  v=u+at        (I)

Here, u is the initial velocity, a is the acceleration, s is the height, and t is the time interval.

Conclusion:

Substitute 0 for u, 3.965 for t, 9.8m/s2 for a in expression (I)

  vy=u+atvy= 0 +9.8×3.965=38.857 m/s

And the velocity along vx= 13.595 m/s

The magnitude of the velocity,

  |v|= (13.595 m/s)2+(38.857)2= 41.167 m/s

Write the direction will then be,

   θ=tan1(vyvx) θ=tan1(38.9 m/s13.6 m/s)θ=70.72°

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Chapter 4 Solutions

College Physics, Volume 1

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