1) A 90-kg astronaut is space-walking outside the space capsule and is stationar

Question

1) A 90-kg astronaut is space-walking outside the space capsule and is stationary when the tether line breaks. As a means of returning to the capsule he throws his 5.2-kg space hammer at a speed of 19 m/s away from the capsule. At what speed does the astronaut move toward the le? E) 5.0 m/s C) 0.78 m/s D) 1.1 m/s A) 0.40 m/s B) 0.31 m/s F) None of these 2) A ball of mass 0.090 kg is shot from a spring-loaded gun and becomes inelastically embedded in a pendulum of mass 0.910 kg. The muzzle velocity was 18.0 m/sec. How high did the pendulum rise? A) 0.13 m B) 0.04 m C) 0.05 m G) None of these D) 0.06 m E) 0.07 m F 0.18 m 3) A mi -50-gram ball moving at some velocity, collides head-on with a stationary ball of mass ma = 100 grams. The collision is elastic and the balls move with velocities vi,--3.33 m/s and v2' +6.7 m/s immediately after the collision. What was the speed of the 50 gm ball immediately before the collision? A) +6.7 m/s B) +3.3 m/s D)-3.3 m/s E) +15 m/s F+10 m/s G) +7.3 m/s H) +13.7 m/s I) None of these C)-6.7 m/s 4) What is the linear speed due to the Earth's rotation of a point in latitude 36.0° N)? The radius of the Earth is RE- 6.38 x 10 m, T 24 hours. A) 522 m/s B) 375 m/s C) 308 m/s D) 618 m/s E) 417 m/s F) None of these 5) A wheel accelerates with a constant angular acceleration of 3.5 rad/s. If the initial velocity is 4.0 rad/s, what is the angular velocity at t-2.0 s? A) 1.0 rad/s B) 8.0 rad/s C) 7.0 rads D) 15 rad/s E) 11 rad/s F) None of these 6) A wheel with moment of inertia, I = (3 4mR2 of radius 0.50 m and a mass of 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical distance of 6.0 m? A) 5.8 m/s B) 3.8 m/s D) 7.7 m/s E) 8.2 m/s F) None of these C) 4.2 m/s

Explanation / Answer

(1) Use conservation of momentum -

m1v1 + m2v2 = 0 (initial momentum)

=> 5.2*19 + 90*v2 = 0

=> v2 = -(5.2*19) / 90 = -1.10 m/s

Hence, option (D) is the correct answer.

(2) Use conservation of momentum to determine the final velocity.

0.090*18 = (0.090+0.910)*V

=> V = (0.090*18) / 1.0 = 1.62 m/s

Suppose the height raised by the pendulum is h meter.

So, we have -

h = V^2 / 2*g = 1.62^2 / (2*9.8) = 0.13 m

So, option (A) is the correct answer.

(3) Apply conservation of momentum -

50*v1 + 100*0 = 50*(-3.33) + 100*(6.7)

=> v1 = 503.5 / 50 = 10.07 m/s = 10.0 m/s

Hence, option (F) is the coorect answer.

As per Chegg guidlines, you can ask the answer of only one question at a time. I have answered the three questions.

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