vertical motion- max height

A rocket is launched from rest at ground level and moves vertically upwards. it rises 100m in the first 5 secondsof its motion. use g=10

The rocket runs out of fuel when it has reached a height of 100m. It can now be modelled as a partical moving vertically under gravity.

a) Find the max height above ground reached by the rocket. Answer is 180m... I cannot get this.

I have calulated the intial acceleration to be 8.

b) The total time taken for the rocket to reach its max height from the moment its launched.

Any help really greatly recieved!!!

Reply 1

username6357534

7

Original post by Mechanicsstudent

A rocket is launched from rest at ground level and moves vertically upwards. it rises 100m in the first 5 secondsof its motion. use g=10

The rocket runs out of fuel when it has reached a height of 100m. It can now be modelled as a partical moving vertically under gravity.

a) Find the max height above ground reached by the rocket. Answer is 180m... I cannot get this.

I have calulated the intial acceleration to be 8.

b) The total time taken for the rocket to reach its max height from the moment its launched.

Any help really greatly recieved!!!

For the remaining part of its journey you have:

s = ? (this is what you need to work and add to the 100m it already attained)
u = ? (calculate it from the first part of its journey. It's its previous final velocity)
v = 0 at its highest point
a = -10
t doesn't matter.

Reply 2

davros

16

Original post by Mechanicsstudent

A rocket is launched from rest at ground level and moves vertically upwards. it rises 100m in the first 5 secondsof its motion. use g=10

The rocket runs out of fuel when it has reached a height of 100m. It can now be modelled as a partical moving vertically under gravity.

a) Find the max height above ground reached by the rocket. Answer is 180m... I cannot get this.

I have calulated the intial acceleration to be 8.

b) The total time taken for the rocket to reach its max height from the moment its launched.

Any help really greatly recieved!!!

as the previous poster says, for the 1st stage of the motion (acceleration = 8) it has reached a height of 100m. When the fuel runs out, its acceleration is now -10 (gravity only) so do a new phase of suvat using v = 0 (at the max point of the motion), and u = whatever the instantaneous velocity was after 5 seconds. This will give you an additional upwards displacement to be added on to the 100m and you should get 180m in total.

vertical motion- max height

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