Solving a Rocket Motion Problem

[drew1989]

Ok here's a question i had for homework, but i am having some trouble with it:

a rocket is fired from rest with an acceleration at=22.8m/s at an elevation angle of theta=62.4. the rocket travels in a straightline for 8.95 seconds, when the fuel runs out. at this time it becomes a projectile and falls back to the ground. fill in the tables

they ask for:

straightline

total horizontal verticle

vi vi vi
vf vf vf
d d d
a a a
t t t

and they ask for

projectile

up down horizontal


my answers were

total horizontal verticle

vi 0 vi 0 vi 0
v 204.06 vf 159.18 vf 147.18
d 913.17 d 809.25 d 423.07
a 22.8 a 20.2 a 10.6
t 8.95 t 7.9 t 4.2

i got these answers by using the pythagorean theorem and using the vf=vi+at formula. if these are right could you tell me, if not tell me what i was doing wrong. after i get to projectile it is easy but i think i made a mistake. would the time be the same for all?

 

[Nate810]

projectileup down horizontalvi 204.06 vi 147.18 vi 159.18vf 0 vf 0 vf 0d 423.07 d 913.17 d 809.25a -10.6 a -20.2 a 0t 4.2 t 7.9 t 7.9Yes, your answers for both tables are correct. The time for each motion would be the same because the rocket travels in a straight line for 8.95 seconds until it runs out of fuel and becomes a projectile.

 

[quicknote]

Your calculations seem to be correct based on the given information. The time for the projectile motion would be the same for both up and down motion since it is only affected by the initial velocity and acceleration, which are the same for both directions. However, the initial velocity for the down motion would be the final velocity from the straightline motion, so it would be 147.18 m/s. Also, for the horizontal motion, the initial velocity would be 204.06 m/s since there is no acceleration in the horizontal direction. Overall, your calculations seem to be correct and you can verify them by using the equations of motion for projectile motion.