Motion in a Plane — Prelims Questions

A projectile is fired from the ground with an initial velocity of $50\,\text{m/s}$ at an angle of $37^\circ$ above the horizontal. Assuming $g = 10\,\text{m/s}^2$ and $\sin37^\circ = 0.6$, $\cos37^\circ = 0.8$, what is the maximum height reached by the projectile?

A particle moves in a circle of radius $R = 2\,\text{m}$ with a constant speed of $4\,\text{m/s}$. What is the magnitude of its centripetal acceleration?

A boat can travel at a speed of $10\,\text{m/s}$ in still water. The river flows at $6\,\text{m/s}$ due east. If the boat wants to cross the river directly to the opposite bank (shortest path), in what direction relative to the bank should it steer?

A particle's position vector is given by $\vec{r}(t) = (3t^2 - 2t)\hat{i} + (4t + 5)\hat{j}$, where $\vec{r}$ is in meters and $t$ is in seconds. What is the velocity vector of the particle at $t = 1\,\text{s}$?

Two projectiles are launched with the same initial speed $u$. If they are launched at angles $30^\circ$ and $60^\circ$ with the horizontal, what is the ratio of their horizontal ranges ($R_1:R_2$)?

A car is moving east at $10\,\text{m/s}$. A person inside the car observes a ball moving north at $5\,\text{m/s}$ relative to the car. What is the velocity of the ball relative to the ground?