Decceleration of a spaceship
A spaceship is going 50 km/s and is 100 km behind another spaceship moving at 20 km/s in the same direction. If the first ship does not deccelerate, the ships will collide in about 3 s. How fast must the spaceship deccelerate to just avoid a collision?
Should I use the collision time of 3 s to find the necessary a to stop in 3 s, or find a such that the ship stops in 100 km?
Answer
This is just a kinematic problem, but it looks more complicated because there are two spaceships. Really, we have a kinematic problem in terms of the distance between the spaceships and the relative velocity between them.
The first ship is traveling at 50 km/s, and the second at 20 km/s, so the relative velocity between them is 30 km/s. There is a separation of 100 km between them, so without decceleration the gap will be closed in
100 / 30 ~ 3.33 seconds.
If the first ship deccelerates, then we want the relative velocities of the ships to be zero after 100 km.
We can formulate the kinematic problem as follows:
distance= 100
v_initial = 30
v_final = 0
Is there a kinematic equation that lets you solve for acceleration from these quantities?
Customer support service by UserEcho
This is just a kinematic problem, but it looks more complicated because there are two spaceships. Really, we have a kinematic problem in terms of the distance between the spaceships and the relative velocity between them.
The first ship is traveling at 50 km/s, and the second at 20 km/s, so the relative velocity between them is 30 km/s. There is a separation of 100 km between them, so without decceleration the gap will be closed in
100 / 30 ~ 3.33 seconds.
If the first ship deccelerates, then we want the relative velocities of the ships to be zero after 100 km.
We can formulate the kinematic problem as follows:
distance= 100
v_initial = 30
v_final = 0
Is there a kinematic equation that lets you solve for acceleration from these quantities?