(Solved): Q13 O Points Tara needs to investigate a train crash. Two trains were erroneously traveling on the ...

Q13 O Points Tara needs to investigate a train crash. Two trains were erroneously traveling on the same track in the same direction. Train A was traveling with constant speed \( v_{1} \) and train B was behind it, traveling with a constant higher speed \( v_{2} \). At some time that Tara assigns to be \( t=0 \), the driver of train \( \mathrm{B} \) notices train \( \mathrm{A} \) and starts braking with acceleration \( \beta t \) where \( \beta \) is a constant known to Tara, and \( t \) is time. If the records show that a time \( t_{1} \) had elapsed from the start of the braking to the crash, what is the distance \( d \) between the trains at the time the driver of train \( \mathrm{B} \) starts to brake? Q14 O Points At \( t=0 \) an old steam train is moving with a known velocity of magnitude \( v_{0}=5 \mathrm{~m} / \mathrm{s} \) in the positive \( x \)-direction with a known, constant acceleration of \( a_{C}=0.5 \mathrm{~m} / \mathrm{s}^{2} \). After 5 minutes have passed, the train is at \( x=L=300 \mathrm{~m} \). At that moment the conductor notices a bus stuck on the track a known distance of \( D=1.5 \mathrm{~km} \) away. The conductor engages a brake which slows the train at the unknown constant rate of magnitude \( a_{B} \). The train stops just as it reaches the bus. Q15.1 Part (a) 0 Points (a) Find the velocity and position of the rocket for all times \( t \geq 0 \). Q15.2 Part (b) O Points (b) What is the maximum height the rocket will reach? Q15.3 Part (c) O Points (c) How long until the rocket returns to the ground? Q15.4 Part (d) O Points (d) What is the minimum height, \( H \), necessary for the rocket to safely launch? O Points (a) Find the velocity and position of the train for all times \( t \geq 0 \). Q14.2 Part (b) O Points (b) Determine what \( a_{B} \) must equal for the train to stop just as it reaches the bus. Q15 O Points A model rocket is initially a height of \( H=2.00 \mathrm{~m} \) above the ground. At \( t=0 \), it is released from rest and has its engines ignited. Its engines generate an acceleration in the positive \( y \) direction which changes with time of magnitude \( \beta t \), where \( \beta=18.00 \mathrm{~m} / \mathrm{s}^{3} \). This acceleration doesn't include the effects of gravity. After \( 5.00 \) seconds have passed, the rocket's fuel will run out, and will no longer provide an upward thrust.