Question

A rocket is launched upward with an acceleration of 100 m/s. Eight seconds later the fuel is exhausted. Find
a. The highest velocity the rocket attains.
b. The maximum altitude
c. The total time of flight and
d. The velocity with the rocket strikes the ground.

Answer 1

How do I solve this?

Answer 2

Ready? We'll take it one by one okay?

Answer 3

ok.

Answer 4

For the first one we know the rocket is at rest before launching so initial velocity is zero. We have acceleration and time thus we can use the equation v=u+at to get the highest velocity attained by the rocket.

Answer 5

U is initial velocity in that equation.

Answer 6

v=800?

Answer 7

Yes.

Answer 8

How do I solve for the maximum altitude?

Answer 9

Ok, we can use the equation y=ut-1/2gt^2

Answer 10

Initial velocity is zero here, and so the equation reduces to 1/2gt^2 slotting in values it becomes, 4.9*64=313.6m.

Answer 11

What equation will I use to solve for the total time of flight?

Answer 12

Okay now the rocket has reached a certain height, the velocity becomes zero at the highest point and the rocket starts to fall down with acceleration due to gravity (9.8m/s^2) through the same distance d=313.6 metres. So we can still use the same equation y=ut+1/2gt^2.

Answer 13

So when you get the time it takes to fall through this distance add it to the other time given to you and that's your time of flight!

Answer 14

Ok. How about the velocity when it strikes the ground?

Answer 15

Umm before I proceed I hope all of these makes sense to you.

Answer 16

Yes, please proceed.

Answer 17

The velocity with which the rocket strikes the ground is the final velocity, and we know that its initial velocity is zero and its falling through a distance of 313.6m with acceleration 9.8mls^2 so we can use the equation v^2=u^2+2ad to get V.

Answer 18

v^2=6146.56 ?

Answer 19

Yes sir.

Answer 20

Then you take the square root of 6146.56 which gives you 78.4mls.

Answer 21

Thank you so much :)

Answer 22

No problems sir.