1
$\begingroup$

I have a homework problem that deals with solving the integral of a given vector. It sets the vector equal to an equation and then puts it inside of a definite integral and calls this a new vector $\vec{r}$, representing the displacement. I know that I should solve for the integral, but when I did, the answer was incorrect. Is there something that I am missing?

Here is the problem:

After a ball rolls off the edge of a horizontal table at time $t = 0$, its velocity as a function of time is given by: $$\vec{v} = 1.0 \hat{i} − 9.8t \hat{j}$$ where $v$ is in meters per second and $t$ is in seconds. The ball's displacement away from the edge of the table, during the time interval of $0.320\mathrm{s}$ for which the ball is in flight, is given by: $\vec{Δr}$ = the integral from $0.320$ to $0$ of $v dt$.

To perform the integral, you can use the calculus theorem The integral of $[A + B f(x)] dx$ = the integral of $A dx + B$ times the integral $f(x) dx$.

You can think of the units and unit vectors as constants, represented by $A$ and $B$. Perform the integration to calculate the displacement of the ball from the edge of the table at $0.320\mathrm{s}$.

$\endgroup$

closed as off-topic by user108787, ACuriousMind, Gert, John Rennie, Qmechanic Sep 3 '16 at 14:26

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "Homework-like questions should ask about a specific physics concept and show some effort to work through the problem. We want our questions to be useful to the broader community, and to future users. See our meta site for more guidance on how to edit your question to make it better" – Community, ACuriousMind, Gert, John Rennie, Qmechanic
If this question can be reworded to fit the rules in the help center, please edit the question.

0
$\begingroup$

You may proceed to calculate $\Delta \vec r(t) = \int_{0}^t dt'\,\vec v(t)$ via standard integration. Note that the integral is applied to each component of the velocity vector: $\int dt\,\vec v(t) = (\int dt\,v_x(t),\int dt\, v_y(t))$.

$\endgroup$

Not the answer you're looking for? Browse other questions tagged or ask your own question.