Question

how to find the height of a rocket being launched with the following information.
mass=667.1g acceleration=28.75m/s force=19142.9N time=2sec height=? angle=37 degress

Answer 1

first draw a free body diagram

Answer 2

we know weight= mass*gravity acceleration or
w=mg

Answer 3

for the force you have to break it into x and y components
Fx=Fcos
Fy=Fsin

Answer 4

the angle would be the angle it is launched at which is given to be 37 degrees

Answer 5

now you find the net force for each direction so
Fnety= Fy-W
Fnetx=Fx

Answer 6

with this you can use F=ma to find a and then plug it into
s=vit+1/2at^2 since its initial velocity is zero we can leave that out and we have
s=1/2at^2

Answer 7

@lexy148 is the initial speed of your rocket equals to zero?

Answer 8

ok! the initial speed along z-axis, namely vertical axis, of your rocket has magnitude equals to 34.54 m/s, are you agree?

Answer 9

provided that:

Answer 10

now the times at which your rocket will reaches its maximum height, is:
\[\tau=\frac{ v _{0z} }{ g }=\frac{ 34.54 }{ 9.81 }=3.52 secs\]

Answer 11

and its maximim height h is:
\[h=\frac{ v _{0z}^{2} }{ 2g }=\frac{ (34.54)^{2} }{ 19.6 }\approx 60.9 meters\]

Answer 12

formulae:
\[h=-\frac{ 1 }{ 2 }g \tau ^{2}+v _{0z}\tau \]

Answer 13

how to calculate the initial speed, it' simple I have used this formula:
\[F*\sin(37°)*\tau=m*v _{0z}\]

Answer 14

it asks for the time after 2 secs, not the maximum height.

BUT @Michele_Laino You are providing a complete solution, which really does not help the OP to understand the concepts.

Please offer help and hints, but let the OP DO the calculations, and derive the relationships for themselves.
Otherwise you just give them the answer to THIS question - and the next one will not have the same answer!

Answer 15

also @Michele_Laino
the initial speed is assumed to be 0 (the rocket is 'launched') so your work above seems to be inaccurate on at least 2 counts.

Answer 16

@MrNood, Sorry you are right!