Need help with integration position vector question

[P-Jay1]

Hi, can anyone help me with this question? Or give me some helpful links. I'm stuck!

It's question B2 part b. Thanks.

View attachment PHY116.pdf

 

[HallsofIvy]

What is your difficulty? You are given an acceleration vector $-g\vec{j}$ and, I presume, you know that the velocity vector is the integral of that $-gt\vec{j}+ \vec{v}(0)$ where $\vec{v}(0)$ is the "initial velocity" vector. You are given that by being told it has "magnitude v at an angle $\theta$ to $\vec{i}$". Do you know how to write such a vector at that angle? (Think about the lengths of the legs of a right triangle with hypotenus of length v and one angle $\theta$.)

Once you have $\vec{v}(0)$ add it to $-gt\vec{j}$ to get the velocity vector as a function of t and integrate again.

 

[P-Jay1]

This has answered my question. Thankyou!