Physics
Physics
5th Edition
ISBN: 9781260486919
Author: GIAMBATTISTA
Publisher: MCG
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Chapter 3, Problem 50P

(a)

To determine

The change in velocity during the trip.

(a)

Expert Solution
Check Mark

Answer to Problem 50P

The change in velocity during the trip is Δv=176km/h at 24°south of the east_.

Explanation of Solution

Consider the figure 1 showing initial and final velocities

Physics, Chapter 3, Problem 50P

Let +x be the east direction, and +y be he north direction.

Write the expression for change in velocity

Δv=vfvi (I)

Here, Δv is the change in velocity, vf is the final velocity, and vi is the initial velocity

Write the expression for magnitude of change in velocity

|Δv|=(Δvx)2+(Δvy)2 (II)

Write the expression for direction of change in velocity

θ=tan1(oppositeadjacent)=tan1(vyvx) (III)

Conclusion:

Substitute 100km/h for vf, and 90km/h for vi in equation (I)

Δv=100km/h(SE)90km/h(W) (IV)

If west changes to east, equation (IV) become

Δv=100km/h(SE)+90km/h(E) (V)

The x and y component of velocity are

vx=(100km/h)cos315°+90km/h (VI)

vy=(100km/h)sin315° (VII)

Substitute equation (VI) and (VII) in (II)

|Δv|=((100km/h)cos315°+90km/h)2+((100km/h)sin315°)2=176km/h

Substitute equation (VI) and (VII) in (III)

θ=tan1((100km/h)sin315°(100km/h)cos315°+90km/h)=24°=24°south of east

Therefore, the change in velocity during the trip is Δv=176km/h at 24°south of the east_.

(b)

To determine

The average acceleration during the trip.

(b)

Expert Solution
Check Mark

Answer to Problem 50P

The average acceleration during the trip aav=284km/h2at 24°south of east_.

Explanation of Solution

Write the expression of change in time for the three distances

Δt=d1v1+d2v2+d3v3 (I)

Here, d1 is the distance travelled in west direction, v1 is the velocity in west direction, d2 is the distance travelled in south direction, v2 is the velocity in south direction, d3 is the distance travelled in south east direction, and v3 is the velocity in south east direction

Write expression for average velocity

aav=ΔvΔt (II)

Here aav is the average velocity, Δv is the change in velocity, Δt is the change in time

Conclusion:

Substitute 16km for d1, 8km for d2, 34km for d3, 90km/h for v1, 80km/h for v2, and 100km/h in equation (I)

Δt=16km90km/h+8km80km/h+34km100km/h=0.62h

Substitute 176km/hat 24°south of east for Δv, and 0.62h in equation (II)

aav=176km/hat 24°south of east0.62h=284km/h2

Therefore, the average acceleration during the trip aav=284km/h2at 24°south of east_.

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