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Chapter 8: Q43PE (page 291)

During a circus act, an elderly performer thrills the crowd by catching a cannon ball shot at him. The cannon ball has a mass of\(10.0kg\)and the horizontal component of its velocity is\(8.00 m/s\)when the\(65.0kg\)performer catches it. If the performer is on nearly frictionless roller skates, what is his recoil velocity?

Short Answer

Expert verified

The velocity of the system after collision will be \(1.07 m/s\).

Step by step solution

01

Definition of collision

According to collision theory, only a specific number of collisions between acceptable reactant particles with the correct orientation result in a detectable or noticeable change; these successful modifications are referred to as successful collisions.

02

Given data

The velocity of cannon ball is \({v_c} = 8.00 m/s\)in right side.

The mass of the cannon ball is\({M_c} = 10.0kg\).

The velocity of the person is\({v_p} = 0\)

The mass of the person is\({M_p} = 65kg\)

The Collison is inelastic.

03

Velocity of the system of players after the collision

By putting all the value into the equation we get

\(\begin{aligned}{M_c}{V_c} + {M_p}{V_p} &= + {M_T}{V_f}\\{V_f} &= \dfrac{{{M_v}{V_c} + {M_p}{V_p}}}{{{M_T}}}\\{V_f} &= \dfrac{{\left( {10} \right)\left( 8 \right) + \left( {65} \right)\left( 0 \right)}}{{\left( {10 + 65} \right)}}\\{V_f} &= 1.07\,m/s\end{aligned}\)…………………(1)

Hence the velocity of the system after collision will be\(1.07 m/s\). They will move towards right side as the velocity answer is positive.

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Most popular questions from this chapter

One of the waste products of a nuclear reactor is plutonium\( - 239\left( {^{239}Pu} \right)\). This nucleus is radioactive and decays by splitting into a helium-\(4\)nucleus and a uranium\( - 235\)nucleus\(\left( {^4He{ + ^{235}}U} \right)\), the latter of which is also radioactive and will itself decay some time later. The energy emitted in the plutonium decay is\(8.40 \times 1{0^{ - 13}}\;J\)and is entirely converted to kinetic energy of the helium and uranium nuclei. The mass of the helium nucleus is\(6.68 \times 1{0^{ - 27}}kg\),while that of the uranium is\(3.92 \times 1{0^{ - 25}}\;kg\)(note that the ratio of the masses is\(4\)to\(235\)). (a) Calculate the velocities of the two nuclei, assuming the plutonium nucleus is originally at rest. (b) How much kinetic energy does each nucleus carry away? Note that the data given here are accurate to three digits only.

During an ice show, a\(60kg\)skater leaps into the air and is caught by an initially stationary\(75kg\)skater. (a) What is their final velocityassuming negligible friction and that the\(60kg\)skater’s originalhorizontal velocity is\(4\;.00m/s\)? (b) How much kinetic energy is lost?

Ernest Rutherford (the first New Zealander to be awarded the Nobel rize in Chemistry) demonstrated that nuclei were very small and dense by scattering helium-4 nuclei\(\left( {{}^4He} \right)\)from gold-197 nuclei\(\left( {{}^{197}Au} \right)\).The energy of the incoming helium nucleus was\(8.00 \times {10^{ - 13}}\;{\rm{J}}\), and themasses of the helium and gold nuclei were\(6.68 \times {10^{ - 27}}\;{\rm{kg}}\)and\(3.29 \times {10^{ - 25}}\;{\rm{kg}}\), respectively (note that their mass ratio is 4 to 197). (a) If a helium nucleus scatters to an angle of\(120^\circ \)during an elastic collision with a gold nucleus, calculate the helium nucleus’s final speed and the final velocity (magnitude and direction) of the gold nucleus. (b) What is the final kinetic energy of the helium nucleus?

Starting with equations\({m_1}{v_1} = {m_1}{v_1}^\prime \cos {\theta _1} + {m_2}{v_2}^\prime \cos {\theta _2}\)and\(0 = {m_1}{v_1}^\prime \sin {\theta _1} + {m_2}{v_2}^\prime \sin {\theta _2}\)for conservation of momentum in the x- and y-directions and assuming that one object is originally stationary, prove that for an elastic collision of two objects of equal masses, 1/2mv12 = 1/2mv’12 + 1/2mv’22 + mv’1v’2cos (ɵ1 - ɵ2)as discussed in the text.

What is the acceleration of a \[5000\;kg\]rocket taking off from the Moon, where the acceleration due to gravity is only \[1.6\;m/{s^2}\], if the rocket expels \[8.00\;kg\] of gas per second at an exhaust velocity of \[{\rm{2}}{\rm{.20 \times 1}}{{\rm{0}}^{\rm{3}}}\;{\rm{m/s}}\]?
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