Question

Two rockets are fired at each other with initial velocities of 150m/s150m/s and are 6000m6000m apart. The first rocket is accelerating at 5m/s25m/s2 while the second is accelerating at 15m/s215m/s2 . How far has the second rocket gone (in meters) when they collide? A :

Answer 1

3469.788 m

Step-by-step explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement

a = Acceleration

First rocket

`s=ut+(1)/(2)at^2\\\Rightarrow s=150* t+(1)/(2)* 5* t^2\\\Rightarrow s=150t+2.5t^2\ m`

Second rocket

`s=ut+(1)/(2)at^2\\\Rightarrow s=150* t+(1)/(2)* 15* t^2\\\Rightarrow s=150t+7.5t^2\ m`

When this will collide the total distance they would have covered would be 6000 m.

`6000=150t+2.5t^2+150t+7.5t^2\\\Rightarrow 6000=300t+10t^2\\\Rightarrow 10t^2+300t-6000=0`

`t=5\left(√(33)-3\right),\:t=-5\left(3+√(33)\right)\\\Rightarrow t=13.72, -43.72`

Hence at 13.72 seconds they will collide assuming they are launched at the same time.

`s=150t+7.5t^2\\\Rightarrow s=150* 13.72+7.5* 13.72^2\\\Rightarrow s=3469.788\ m`

The second rocket would have gone 3469.788 m when they collide