DP Mathematics: Applications and Interpretation Questionbank

Find the velocity vector at time $t$.

Show that the magnitude of the velocity of the ice-skater at time $t$ is given by

$a {\text{e}}^{bt}\sqrt{\left(1+b^2\right)}$.

Find the magnitude of the velocity of the ice-skater when $t=2$.

Find the value of $a$ and the value of $b$.

At a point $\text{P}$, the ice-skater is skating parallel to the $y$-axis for the first time.

Find $\text{OP}$.

Find an expression for the velocity of $P_1$ at time $t$.

Particle $P_2$ also moves in a straight line. The position of $P_2$ is given by $\mathit{r}=\left(\begin{array}{c}-1\\ 6\end{array}\right)+t\left(\begin{array}{c}4\\ -3\end{array}\right)$.

The speed of $P_1$ is greater than the speed of $P_2$ when $t>q$.

Find the value of $q$.

Find the speed of the helicopter.

Find the distance of the helicopter from the communications tower at $t=0$.

Find the bearing on which the helicopter is travelling.

Find an expression for the acceleration of the ball at time $t$.

Show that the ball is moving in a circle with its centre at $\text{O}$ and state the radius of the circle.

Hence show that the velocity of the ball is always perpendicular to the position vector of the ball.

Find an expression for the velocity of the ball at time $t$.

Find the value of $t$ at the instant the string breaks.

How many complete revolutions has the ball completed from $t=0$ to the instant at which the string breaks?

Assuming the submarine travels in a straight line, write down an equation for the line along which it travels.

Find $\text{OP}$.

Find the coordinates of $\text{P}$.

Find the value of $t$ when the ship will be closest to the lighthouse.

Find the position vector $\overrightarrow{\text{OS}}$ of the ship at time $t$ hours.

An alarm will sound if the ship travels within $20$ kilometres of the lighthouse.

State whether the alarm will sound. Give a reason for your answer.

Find the velocity vector of $P$.

Show that the acceleration vector of $P$ is never parallel to the position vector of $P$.

Find the initial speed of the ball.

Find the angle of elevation of the ball as it is launched.

For the path of the ball, find an expression for $y$ in terms of $x$.

find the value of $a$;

determine the coordinates of the point of intersection P.