Worksheet: Finding Momentum Using Vectors

In this worksheet, we will practice calculating the momentum of a particle of mass m moving in a straight line with velocity v by using vectors.

Q1:

A body of mass 7 kg is moving in a straight line. Its position vector at a time 𝑡 is given by the relation ⃑ 𝑟 ( 𝑡 ) =  𝑡 + 5  ⃑ 𝑖 +  𝑡 + 𝑡  ⃑ 𝑗 2 3 , where ‖ ‖ ⃑ 𝑟 ‖ ‖ is measured in metres and 𝑡 in seconds. Determine the body’s momentum after 2 seconds.

  • A 5 6 ⃑ 𝑖 + 8 4 ⃑ 𝑗
  • B 2 8 ⃑ 𝑖 + 8 5 ⃑ 𝑗
  • C 1 4 ⃑ 𝑖 + 1 3 ⃑ 𝑗
  • D 2 8 ⃑ 𝑖 + 9 1 ⃑ 𝑗

Q2:

A body of variable mass is moving along a fixed straight line. Its mass at time 𝑡 is given by the relation 𝑚 ( 𝑡 ) = 5 𝑡 + 7 and its displacement is given by the relation ⃑ 𝑠 ( 𝑡 ) = ( 5 𝑡 + 4 𝑡 ) ⃑ 𝑖 2 , where ⃑ 𝑖 is a unit vector parallel to the direction of its motion. Determine the body’s momentum ⃑ 𝐻 ( 𝑡 ) and the force that is acting on it ⃑ 𝐹 ( 𝑡 ) .

  • A ⃑ 𝐻 ( 𝑡 ) = ( 5 0 𝑡 + 7 0 𝑡 + 2 8 ) ⃑ 𝑖 2 , ⃑ 𝐹 ( 𝑡 ) = ( 1 0 0 𝑡 + 7 0 ) ⃑ 𝑖
  • B ⃑ 𝐻 ( 𝑡 ) = ( 2 5 𝑡 + 5 5 𝑡 + 2 8 ) ⃑ 𝑖 2 , ⃑ 𝐹 ( 𝑡 ) = ( 5 0 𝑡 + 5 5 ) ⃑ 𝑖
  • C ⃑ 𝐻 ( 𝑡 ) = ( 5 0 𝑡 + 9 0 𝑡 + 2 8 ) ⃑ 𝑖 2 , ⃑ 𝐹 ( 𝑡 ) = ( 5 0 𝑡 + 7 0 ) ⃑ 𝑖
  • D ⃑ 𝐻 ( 𝑡 ) = ( 5 0 𝑡 + 9 0 𝑡 + 2 8 ) ⃑ 𝑖 2 , ⃑ 𝐹 ( 𝑡 ) = ( 1 0 0 𝑡 + 9 0 ) ⃑ 𝑖

Q3:

Determine the mass of a body whose momentum is 37 kg⋅m/s, given that its displacement vector is given by the relation s i j ( 𝑡 ) = ( − 3 𝑡 ) + ( 4 𝑡 ) , where | | s is measured in metres and 𝑡 in seconds.

Q4:

A body of mass 3 kg is moving in a straight line. Its position vector at a time 𝑡 is given by the relation ⃑ 𝑟 ( 𝑡 ) =  𝑡 + 5  ⃑ 𝑖 +  𝑡 + 𝑡  ⃑ 𝑗 2 3 , where ‖ ‖ ⃑ 𝑟 ‖ ‖ is measured in metres and 𝑡 in seconds. Determine the body’s momentum after 3 seconds.

  • A 5 4 ⃑ 𝑖 + 8 1 ⃑ 𝑗
  • B 1 8 ⃑ 𝑖 + 8 2 ⃑ 𝑗
  • C 9 ⃑ 𝑖 + 2 8 ⃑ 𝑗
  • D 1 8 ⃑ 𝑖 + 8 4 ⃑ 𝑗

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