Physics
Physics
3rd Edition
ISBN: 9780073512150
Author: Alan Giambattista, Betty Richardson, Robert C. Richardson Dr.
Publisher: McGraw-Hill Education
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Chapter 4, Problem 173P

(a)

To determine

The distance between the astronaut and asteroid.

(a)

Expert Solution
Check Mark

Answer to Problem 173P

The distance between the astronaut and asteroid is 19m.

Explanation of Solution

The mass of the astronaut is 60.0kg, the initial speed of both astronaut and asteroid is 0m/s, the mass of the asteroid is 40.0kg, the force on the asteroid and astronaut is 250N, the time taken during the application of force is 0.35s and time taken after the force is 5.00s.

Write the expression to calculate the acceleration of the astronaut.

a=FM

Here, a is the acceleration of the astronaut, F is the force on the astronaut and M is the mass of the astronaut.

Substitute 250N for F and 60.0kg for M in the above equation to calculate a.

a=250N60.0kg=4.17m/s2

Write the expression to calculate the acceleration of the asteroid.

a=Fm

Here, a is the acceleration of the asteroid, F is the force on the asteroid and m is the mass of the asteroid.

Substitute 250N for F and 40.0kg for a in the above equation to calculate a.

a=250N40.0kg=6.25m/s2

Write the expression to calculate the distance travelled by the astronaut.

x=ut+12at2

Here, x is the distance moved by the astronaut, u is the initial speed of the astronaut and t is the time taken during the application of force.

Substitute 0m/s for u, 4.17m/s2 for a and 0.35s for t in the above equation to calculate x.

x=(0m/s)(0.35s)+12(4.17m/s2)(0.35s)2=0m+0.255m=0.255m

Write the expression to calculate the distance travelled by the asteroid.

x=ut+12at2

Here, x is the distance moved by the asteroid, u is the initial speed of the asteroid and t is the time taken during the application of force.

Substitute 0m/s for u, 6.25m/s2 for a and 0.35s for t in the above equation to calculate x.

x=(0m/s)(0.35s)+12(6.25m/s2)(0.35s)2=0m+0.383m=0.383m

Write the expression to calculate the speed of the astronaut.

v=u+at

Here, v is the speed of the astronaut.

Substitute 0m/s for u, 4.17m/s2 for a and 0.35s for t in the above equation to calculate v.

v=0m/s+(4.17m/s2)0.35s=1.46m/s

Write the expression to calculate the speed of the asteroid.

v=u+at

Here, v is the speed of the astronaut.

Substitute 0m/s for u, 6.25m/s2 for a and 0.35s for t in the above equation to calculate v.

v=0m/s+(6.25m/s2)0.35s=2.19m/s

Write the expression to calculate the distance moved by the astronaut for 5.00s.

s=vT

Here, s is the distance moved by the astronaut and T is the time taken after the force.

Substitute 5.00s for T and 1.46m/s for v in the above equation to calculate s.

s=1.46m/s(5.00s)=7.30m

Write the expression to calculate the distance moved by the asteroid for 5.00s.

s=vT

Here, s is the distance moved by the asteroid.

Substitute 5.00s for T and 2.19m/s for v in the above equation to calculate s.

s=2.19m/s(5.00s)=10.95m

Write the expression to calculate the distance between the astronaut and asteroid.

X=x+x+s+s

Here, X is the distance between astronaut and asteroid.

Substitute 0.255m for x, 0.383m for x, 7.30m for s and 10.95m for s in the above equation to calculate X.

X=0.255m+0.383m+7.30m+10.95m=18.888m19m

Conclusion:

Therefore, the distance between the astronaut and asteroid is 19m.

(b)

To determine

The relative speed between astronaut and asteroid.

(b)

Expert Solution
Check Mark

Answer to Problem 173P

The relative speed between astronaut and asteroid is 3.65m/s.

Explanation of Solution

Both are travelling in opposite direction. Thus the speed with respect one another is the sum of the speed of individual one.

Write the expression to calculate the relative speed between astronaut and asteroid.

V=v+v

Here, V is the relative speed between astronaut and asteroid.

Substitute 1.46m/s for v and 2.19m/s for v in the above equation to calculate V.

V=1.46m/s+2.19m/s=3.65m/s

Conclusion:

Therefore, the relative speed between astronaut and asteroid is 3.65m/s.

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Chapter 4 Solutions

Physics

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