How do I go about this [projectile motion]

[IntellectIsStrength]

A rocket is launched with an initial velocity of 75.0 m/s [53 degreess above the horizontal]. It goes for 25.0 s along its initial line of motion with an overall acceleration of 25 m/s^2. At this time the rockets fail and the rocket follows a projectile path. Find the total time, dy, and dx, in no particular order.

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so would the vx and vy be:

vx=700cos53 m/s
vy=700sin53 m/s

(700 is the vf of the rocket after 25.0 s, before getting into a projectile path; so is it correct to assume that 700 is the vi for the projectile?)

And so far I've come up with dy = tan θ + ½ a (dx/ Vicosθ)^2... I really don't know what to do next...

 

[Diane_]

I'm not sure exactly what work you're showing or where you got the answers you give, so let me give you some general advice here.

Notice that the conditions of the problem change partway through. That means you're pretty much going to have to solve the problem in two parts.

During the first part, the rocket starts with the initial velocities you have worked out. It also has an "overall acceleration" of 25 m/s^2. I presume that means the net acceleration, and that gravity has been taken into account, so you'll need to split the acceleration into its horizontal and vertical components and figure out from that the horizontal and vertical distances traveled as well as the final horizontal and vertical speeds.

When the rocket engines cut off, the second part of the problem begins. Now you'll use the final velocities you worked out in the first part as the initial velocities in a free fall problem. The rocket will be rising at thus and such a rate - how long until it hits the ground? Obviously, to get that you'll need to know the initial height, which will be the vertical distance you determined in the first part.

Does this help?

Oh - and for the record, I suspect you'd have to take into account the curvature of the Earth to get an accurate answer to this question, but I think I also wouldn't worry about that if I were you. I'd just use it to tease my teacher. :)

 

[quicknote]

Hello,

To solve this problem, we can use the equations of projectile motion. First, let's find the initial velocity components in the x and y directions:

vx = 75.0 m/s * cos(53 degrees) = 45.0 m/s
vy = 75.0 m/s * sin(53 degrees) = 60.0 m/s

Now, we can use the equations of projectile motion to find the total time, dy, and dx. The equations we will use are:

dy = vy * t + 1/2 * a * t^2
dx = vx * t
vy = vy_initial + a * t

We know that the rocket will follow a projectile path after 25 seconds, so we can use that information to solve for the total time:

25 seconds = t

Now, let's use the equation for dy to find the vertical displacement at this time:

dy = (60.0 m/s) * (25 seconds) + 1/2 * (25 m/s^2) * (25 seconds)^2
dy = 1500 m + 3125 m
dy = 4625 m

Next, we can use the equation for dx to find the horizontal displacement at this time:

dx = (45.0 m/s) * (25 seconds)
dx = 1125 m

So, the total time is 25 seconds, the vertical displacement is 4625 m, and the horizontal displacement is 1125 m.

I hope this helps! Let me know if you have any further questions.