Vectors and Projectile

Question

A rocket is launched straight up into the air. If its entire flight takes 5 seconds...

A) What is the initial velocity of the rocket?

B) What is the maximum height the rocket reaches?

Answer 1

Be sure to pause the video at any time if you are taking notes on the how to do this problem.

Have a good night!

I hope this helps!

Answer 2

Hi Hiradetsi!

There are a couple of ways to approach this problem, and Cesar R. suggested one approach in the comments.

I'll suggest another. Is there any difference between the amount of time it takes for the rocket to reach its highest point and the time it takes for it to fall back down? In fact no - those two times are equivalent.

Think about the velocity at the very top of the rocket's trajectory - it must be 0 (can you explain why?). We know that the velocity of the rocket is given by v(t) = v₀ - gt. Now, since we know that the time it takes for the rocket to reach the highest point is the same as it takes for it to fall back down, we know that it takes 5/2 = 2.5 seconds for the rocket to reach its highest point. This allows us to solve for the original velocity, using 0 = v₀ -9.8t.

Once we have the initial velocity, we can plug this into our usual equation y = y₀ + v₀t - .5gt². What time do you think you should plug in?