Question

You are coasting on your 6-kg bicycle at 16 m/s and a 6.0-g bug splatters on your helmet. The bug was initially moving at 2.5 m/s in the same direction as you. If your mass is 45 kg, answer the following questions:

1. What is your change in velocity due to the collision the bug? Mind the sign of your answer; to enter your answer in scientific notation, use the "E notation" (to enter 3.14×10−53.14×10-5, enter "3.14E-5").
   Δv=Δv=  m/s
2. What would the change in velocity have been if the bug were traveling in the opposite direction? Mind the sign of your answer; to enter your answer in scientific notation, use the "E notation" (to enter 3.14×10−53.14×10-5, enter "3.14E-5").
   Δv=Δv=

Answer 1

Solution of A:

We are given,

the mass of bicycle is:

and mass of bicycle rider:

therefore, the total mass of bicycle and rider is:

Mass of the bug is:

Initial velocity of rider is:

and the initial velocity of bug is:

Since bicycle rider and bug both are traveling in the same direction, the inelastic collision and conservation of linear momentum is given by:

Here,

is the initial linear momentum of bicycle and rider
is the initial linear momentum of bug
is the final linear momentum of bicycle and rider
is the final linear momentum of bug

is the final velocity of bicycle and rider
is the final velocity of the bug

Since the bug splattered on helmet, its would have fallen down after splattering so its final velocity is zero

Therefore change in the velocity when bug splatters and it is in the same direction with bicycle rider:

Solution of B:

Since bicycle rider and bug both are traveling in the opposite direction, the inelastic collision and conservation of linear momentum is given by:

Since the bug splattered on helmet, it would have fallen down after splattering so its final velocity is zero

Therefore change in the velocity when bug splatters and it is in the opposite direction with bicycle rider: