Exam 3: Motion in Two Dimensions

The site from which an airplane takes off is the origin. The x axis points east; the y axis points straight up. The position and velocity vectors of the plane at a later time are given by: $\overrightarrow{\mathbf{r}}=\left(1.61 \times 10^{6} \hat{\mathbf{i}}\right) \mathrm{m}$ and $\overrightarrow{\mathbf{v}}=+100 \hat{\mathbf{i}} \frac{\mathrm{~m}}{\mathrm{~s}}$ .The plane is most likely:

A car is driven 1200 m north at 20.0 m/s and then driven 1600 m east at 25.0 m/s. What are the magnitude and direction of the displacement for this trip?

The vector $\overrightarrow{\mathbf{r}}$ indicates the instantaneous displacement of a projectile from the origin. At the instant when the projectile is at $\overrightarrow{\mathbf{r}}$ , its velocity and acceleration vectors are $\overrightarrow{\mathbf{v}}$ and $\overrightarrow{\mathbf{a}}$ . Which statement is correct?

A tennis player at the Australian Open wants to slam a serve at O so that the ball lands just inside the opposite corner of the court. What should the ratio $\frac{v_{0 y}}{v_{0 x}}$ be for the initial velocity $\overrightarrow{\mathbf{v}}_{0}$ ? The time t = 0 is the time when the ball is hit by the racket.

A space station of diameter 80 m is turning about its axis at a constant rate. If the acceleration of the outer rim of the station is 2.5 m/s2, what is the period of revolution of the space station?