COLLEGE PHYSICS-CONNECT ACCESS
COLLEGE PHYSICS-CONNECT ACCESS
5th Edition
ISBN: 9781260486834
Author: GIAMBATTISTA
Publisher: MCG
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Chapter 4, Problem 46P

(a)

To determine

The horizontal distance from seed pod to point where it hits the ground.

(a)

Expert Solution
Check Mark

Answer to Problem 46P

The horizontal distance is 0.56m.

Explanation of Solution

Write the equation to find the horizontal distance from seed pod to point where it hits the ground.

    Δx=vixtf

Here, Δx is the horizontal distance, vix is the horizontal component of initial velocity and tf is the time of flight.

Since the seed is launched horizontally, initial velocity is equal to the horizontal component of velocity itself. Write the expression for vix.

    vix=v

Here, v is the initial velocity and θ is the angle of projection.

Rewrite the expression for Δx by substituting the above relation.

    Δx=vtf

Write the equation to find tf from vertical component of displacement.

  Δy=viytf+12aytf2

Here, Δy is the vertical displacement, viy is the vertical component of initial velocity and ay is the y-component of acceleration.

Since the seed is launched horizontally, vertical component of initial velocity is zero. y-component of acceleration is gravitational acceleration only.

Conclusion:

Substitute 0m/s for viy, 1.1m for Δy and 9.8m/s2 for ay in the equation to find tf.

  1.1m=(0m/s)tf+12(9.8m/s2)tf2=(4.9m/s2)tf2tf=1.1m4.9m/s2=0.47s

Substitute 1.2m/s for v and 0.47s for tf in the above equation to find Δx.

    Δx=(1.2m/s)(0.47s)=0.56m

Thus, the horizontal distance is 0.56m.

(b)

To determine

The horizontal distance from seed pod to point where it hits the ground if it is projected at 17° from the horizontal.

(b)

Expert Solution
Check Mark

Answer to Problem 46P

The horizontal distance is 0.59m.

Explanation of Solution

Write the expression for vix.

    vix=vcosθ

Here, θ is the angle of projection.

Rewrite the expression for Δx by substituting the above relation.

    Δx=(vcosθ)tf        (I)

tf is divided into parts. First one is the time taken by seed reach the maximum height. Second part is the time take to travel from maximum height to ground.

Consider the first part. Write the equation to find the maximum height of a projectile.

    h=v2sin2θ2g        (II)

Write the equation to find the time taken to reach the height point of motion.

    T=vsinθg        (III)

Here, T is the time take to travel from maximum height to ground.

At the maximum height of projectile motion, vertical component of velocity is zero. Find the time taken to reach the ground from maximum height.

    Δy=viytf+12aytdown2        (IV)

Here, tdown is the time taken to reach the ground from maximum height.

Write the equation for tf.

    tf=T+tdown

Conclusion:

Substitute 1.2m/s for v, 17° for θ and 9.8m/s2 for g in the equation (II) to find h.

    h=(1.2m/s)2(sin17°)22(9.8m/s2)=6.3×103m

Substitute 1.2m/s for v, 17° for θ and 9.8m/s2 for g in the equation (III) to find h.

  T=(1.2m/s)(sin17°)9.8m/s2=0.04s

Substitute 1.1m+6.3×103m for Δy, 0m/s for viy and 9.8m/s2 for ay in equation (IV) to find tdown.

    1.1m+6.3×103m=(0m/s)tf+12(9.8m/s2)tdown21.1063m=(4.9m/s2)tdown2tdown=1.1063m4.9m/s2=0.475s

Substitute 0.475s for tdown and 0.04s for T in the equation to find tf.

    tf=0.04s+0.475s=0.515s

Substitute 1.2m/s for v, 17° for θ and 0.515s for tf in equation (I) to find Δx.

    Δx=(1.2m/s)(cos17°)(0.515s)=0.59m

Thus, the horizontal distance is 0.59m.

(c)

To determine

Check whether the air resistance is negligible in second case or not.

(c)

Expert Solution
Check Mark

Answer to Problem 46P

Role of air resistance is not considered on assuming that it is negligible.

Explanation of Solution

Note that in any of the calculations given, the influence of air drag is not considered. If taken, calculation will be more complex. Air drag is directly proportional to the square of velocity of projectile. Since the velocity of projectile is small, it can be assumed that air drag has no significant role in the projectile motion of seed.

Thus, the role of air resistance is not considered on assuming that it is negligible.

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Chapter 4 Solutions

COLLEGE PHYSICS-CONNECT ACCESS

Ch. 4.4 - Prob. 4.8PPCh. 4.5 - Prob. 4.5ACPCh. 4.5 - Prob. 4.10PPCh. 4.5 - Prob. 4.5BCPCh. 4.6 - Prob. 4.11PPCh. 4.6 - Prob. 4.6CPCh. 4 - Prob. 1CQCh. 4 - Prob. 2CQCh. 4 - Prob. 3CQCh. 4 - Prob. 4CQCh. 4 - Prob. 5CQCh. 4 - Prob. 6CQCh. 4 - Prob. 7CQCh. 4 - Prob. 8CQCh. 4 - Prob. 9CQCh. 4 - Prob. 10CQCh. 4 - Prob. 11CQCh. 4 - Prob. 12CQCh. 4 - Prob. 13CQCh. 4 - Prob. 14CQCh. 4 - Prob. 15CQCh. 4 - Prob. 16CQCh. 4 - Prob. 17CQCh. 4 - Prob. 18CQCh. 4 - Prob. 19CQCh. 4 - Prob. 1MCQCh. 4 - Prob. 2MCQCh. 4 - Prob. 3MCQCh. 4 - Prob. 4MCQCh. 4 - Prob. 5MCQCh. 4 - Prob. 6MCQCh. 4 - Prob. 7MCQCh. 4 - Prob. 8MCQCh. 4 - Prob. 9MCQCh. 4 - Prob. 10MCQCh. 4 - Prob. 11MCQCh. 4 - Prob. 12MCQCh. 4 - Prob. 13MCQCh. 4 - Prob. 14MCQCh. 4 - Prob. 15MCQCh. 4 - Prob. 16MCQCh. 4 - Prob. 17MCQCh. 4 - Prob. 18MCQCh. 4 - Prob. 19MCQCh. 4 - Prob. 20MCQCh. 4 - Prob. 21MCQCh. 4 - Prob. 1PCh. 4 - Prob. 4PCh. 4 - Prob. 5PCh. 4 - Prob. 6PCh. 4 - Prob. 7PCh. 4 - Prob. 8PCh. 4 - Prob. 9PCh. 4 - Prob. 10PCh. 4 - Prob. 11PCh. 4 - Prob. 12PCh. 4 - Prob. 14PCh. 4 - Prob. 15PCh. 4 - Prob. 16PCh. 4 - Prob. 17PCh. 4 - Prob. 18PCh. 4 - Prob. 19PCh. 4 - Prob. 20PCh. 4 - Prob. 21PCh. 4 - Prob. 22PCh. 4 - Prob. 23PCh. 4 - Prob. 24PCh. 4 - Prob. 25PCh. 4 - Prob. 26PCh. 4 - Prob. 27PCh. 4 - Prob. 28PCh. 4 - Prob. 29PCh. 4 - Prob. 30PCh. 4 - Prob. 31PCh. 4 - Prob. 32PCh. 4 - Prob. 33PCh. 4 - Prob. 34PCh. 4 - Prob. 35PCh. 4 - Prob. 36PCh. 4 - Prob. 37PCh. 4 - Prob. 38PCh. 4 - Prob. 39PCh. 4 - Prob. 40PCh. 4 - Prob. 41PCh. 4 - Prob. 42PCh. 4 - Prob. 43PCh. 4 - Prob. 44PCh. 4 - Prob. 45PCh. 4 - Prob. 46PCh. 4 - Prob. 47PCh. 4 - Prob. 49PCh. 4 - Prob. 50PCh. 4 - Prob. 51PCh. 4 - Prob. 52PCh. 4 - Prob. 53PCh. 4 - Prob. 54PCh. 4 - Prob. 55PCh. 4 - Prob. 56PCh. 4 - Prob. 57PCh. 4 - Prob. 58PCh. 4 - Prob. 59PCh. 4 - Prob. 60PCh. 4 - Prob. 61PCh. 4 - Prob. 62PCh. 4 - Prob. 63PCh. 4 - Prob. 64PCh. 4 - Prob. 65PCh. 4 - Prob. 67PCh. 4 - Prob. 68PCh. 4 - Prob. 69PCh. 4 - Prob. 70PCh. 4 - Prob. 71PCh. 4 - Prob. 72PCh. 4 - Prob. 73PCh. 4 - Prob. 74PCh. 4 - Prob. 75PCh. 4 - Prob. 76PCh. 4 - Prob. 77PCh. 4 - Prob. 78PCh. 4 - Prob. 79PCh. 4 - Prob. 80PCh. 4 - Prob. 81PCh. 4 - Prob. 82PCh. 4 - Prob. 83PCh. 4 - Prob. 84PCh. 4 - Prob. 85PCh. 4 - Prob. 86PCh. 4 - Prob. 87PCh. 4 - Prob. 88PCh. 4 - Prob. 90PCh. 4 - Prob. 91PCh. 4 - Prob. 92PCh. 4 - Prob. 93PCh. 4 - Prob. 94PCh. 4 - Prob. 95PCh. 4 - Prob. 97PCh. 4 - Prob. 98PCh. 4 - Prob. 99PCh. 4 - Prob. 100PCh. 4 - Prob. 101PCh. 4 - Prob. 102PCh. 4 - Prob. 103PCh. 4 - Prob. 104PCh. 4 - Prob. 105P
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