Kinematics: Solving Problems with Displacement, Velocity, and Acceleration

[PhysicsBeginner]

Hello everyone, I'm new to this forum. I am kinda having trouble with a physics problem. Could someone please help me out with 3 problems. Thanks.

A rocket is fired vertically with an upward acceleration of 27 m/s2. After 21 s, the engine shuts off and the rocket continues as a free particle until it reaches the ground.
(a) What is the highest point the rocket reaches?
km
(b) What is the total time the rocket is in the air?
s
(c) What is the speed of the rocket just before it hits the ground?
m/s
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Two stones are dropped from the edge of a 200-m cliff, the second stone 1.3 s after the first.
(a) How long after the second stone is dropped will the separation between the two stones be 35 m?
s
(b) At this point, how far below the clifftop is the second stone?
m

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A particle undergoes three successive displacements in a plane, as follows: 2.0 m southwest, 5.0 m east, and 8.0 m in a direction 60.0° north of east. Choose the y-axis pointing north and the x-axis pointing east.
(a) Find the components of the first displacement.
m east and m north
Find the components of the second displacement.
m east and m north
Find the components of the third displacement.
m east and m north
(b) Find the components of the resultant displacement.
m east and m north
(c) Find the magnitude and direction of the resultant displacement.
m at an angle of ° North of East
(d) Find the displacement that would be required to bring the particle back to the starting point.
m i + m j.

I got some fromt the last one correct but am having trouble with the whole concept.

 

[PhysicsBeginner]

Ok so apparently i am suppose to show work which i have done on the problems. I haven't done much work on them except draw the pictures etc... For the first problem i know I'm suppose to use the two main kinematics problems which are: v = v0 + at and x = x0+v0t+.5at^2

For the last problem i got the letters a) and c) but i think i am miscalculating the angle on b) and and completely lost on how to do the other parts.

 

[Doc Al]

Ok so apparently i am suppose to show work which i have done on the problems. I haven't done much work on them except draw the pictures etc... For the first problem i know I'm suppose to use the two main kinematics problems which are: v = v0 + at and x = x0+v0t+.5at^2

Time to get to work! You'll need those kinematic equations. (Here's another that may come in handy: V^2 = V0^2 + 2ax )

For the first problem (the rocket) do it in pieces. How fast is it going after 21 sec? How high is it? After 21 sec, it's just a projectile under gravity.

Give it a try.

 

[PhysicsBeginner]

Time to get to work! You'll need those kinematic equations. (Here's another that may come in handy: V^2 = V0^2 + 2ax )

For the first problem (the rocket) do it in pieces. How fast is it going after 21 sec? How high is it? After 21 sec, it's just a projectile under gravity.

Give it a try.

Ok so i plugged the numbers into the first kinematic problem to get the speed at 21 sec which was 500 m/s. After that i used the 3rd equation listed in the quote above to get how high it went and i got the wrong answer from what it is suppose to be. Anyone know what i am doing wrong?

 

[Doc Al]

Ok so i plugged the numbers into the first kinematic problem to get the speed at 21 sec which was 500 m/s.

Check that one over. If you don't find your mistake, post your calculation.