Calculate the displacement? (Projectile motion problem)

[TarPaul91]

Homework Statement

A projectile is launched at an angle of 60° from the horizontal and lands 99 s later at the same height from which it was launched.
1) What is the initial speed of the projectile (in m/s)?
I already figured this out to be 560.16 m/s
2) What is the maximum altitude (in m)?
- I already figured this out to be 12007 m
3) What is the range (in m)?
- I already figured this out to be 2778 m
4) Calculate the displacement (in m) from the point of launch to the position on its trajectory at 91 s. (Express your answer in vector form. Assume the projectile initially travels in the +x and +y-directions, where the +x-direction is horizontal and the +y-direction is straight up.)
^^^^This is where I got lost

Homework Equations

The Attempt at a Solution

I was able to figure out parts 1-3, but I'm not sure how to calculate the displacement.

 

[Master1022]

Homework Statement

4) Calculate the displacement (in m) from the point of launch to the position on its trajectory at 91 s. (Express your answer in vector form. Assume the projectile initially travels in the +x and +y-directions, where the +x-direction is horizontal and the +y-direction is straight up.)

if we are assuming that acceleration is constant -g, then we can use SUVAT equations to solve this:
$$ \textbf{s} = \textbf{u}t + \frac{1}{2}\textbf{a}t^2$$
becomes
$$ \textbf{s} = \textbf{u}t - \frac{1}{2}\textbf{g}t^2$$

You know what u and g vectors are and you can use components to solve for s... I will leave it there with you. If you need more help, please ask and I am happy to provide more hints.

 

[physics_pi_rate]

Hi
I’ll use two equations to derive something
We know that horizontal direction has no force this velocity remains constant = ucos(theta)
This displacement along x direction is
X=ucos(theta)xtime
Also Y=usin(theta).t -1/2g.t^2
Substitute for t using the first equation to get an equation independent of time
That is known as equation of trajectory.
This specific thing may help you out solving for displacement at 91seconds

 

[verty]

@TarPaul91, your answer for #3 is wrong.

Regarding #4, let P(t) be the location of the projectile at time t. You want to find |P(91) - P(0)|.