How Do You Calculate the Maximum Height of a Rocket Launched at 70 Degrees?

[KiNGGeexD]

Question;

A rocket launched at 70 degrees to the horizontal has constant net acceleration of 8m/s^2 along its path for 6.5 seconds and then is in free fall!

What is the rockets maximum height?
Ps answer is 281m I couldn't help but look lol

Solution attempt:

From the net acceleration I got the velocity as simply the acceleration multiplied by the time
And from that tried to use kinematic equations but got wrong answers every time! This keeps happening with projectile questions! Frustrating!

I think my error could be because net acceleration = change in velocity/ time But I'm not sure!

 

[ehild]

Can you show what you did, please...


ehild

 

[Fineline00]

Concentrate on only the vertical component of acceleration and displacement etc.

You have a resultant acceleration in a given direction, find the acceleration in the direction you need

 

[KiNGGeexD]

So I take the component in the vertical direction?

8sin70= 7.5m/s^2

 

[Fineline00]

Yeah, from there you should be able to get your answer of 281m (which is correct, books can be prone to errors sometimes though)

Remember in free fall that the acceleration would be -9.81ms^2

 

[haruspex]

There's something a bit fishy about the given information. How will the rocket have constant acceleration 'along its path'? If we take the thrust as a vector at 70 degrees to the horizontal, then add gravity, we'll not get an acceleration that is along its path. Is it possible that it means only that the component of its acceleration along its path is 8m/s^2?

 

[ehild]

If you try to read the mind of the problem writer, the net acceleration should mean a vector that makes 70 degrees with the horizontal and of magnitude 8 m/s². That acceleration is the resultant of gravity and that of the thrust.


ehild

 

[haruspex]

If you try to read the mind of the problem writer, the net acceleration should mean a vector that makes 70 degrees with the horizontal and of magnitude 8 m/s². That acceleration is the resultant of gravity and that of the thrust.
ehild

Yes, I suppose it could have fins such that although the engine thrust is along its path it can derive a component to cancel gravity. I still feel it's not entirely unambiguous.