Question 1 Two ships $A$ and $B$ are $10$ miles apart, $A$ being due west of $B$ and steaming due East at $12$ miles per hour. $B$ is steaming due North at $18$ miles per hour. When will they be nearest one another and what will be their distance apart at that time? Question 2... Read More

Question 1 A warship steaming due North at $20$ knots is observed by a submarine $6$ sea-miles North-West of her. The submarine has a speed of $15$ knots. In what direction should the submarine steer to close in one the warship as soon as possible? If she follows that course how long will it take... Read More

Question 1 Prove the formula $v=\omega r$ for uniform motion in a circle. A particle moving in a circle of radius $3$ inches makes $2$ revolutions per second. Find its linear velocity at any instant. Find also the change in the direction of its linear velocity one-twentieth of a second after that instant. Hence find... Read More

Question 1 If two bodies $A$, $B$ are moving velocities $u_1$, $u_2$, in directions inclined at angles, $\theta_1$, $\theta_2$ respectively to the horizontal, find the horizontal and vertical components of the velocity of $A$ relatives to $B$. To a man walking at $3$ miles per hour the rain appears to fall vertically ; when he... Read More

Question 1 A body moves in a plane, its position referred to rectangular axes in the plane after $t$ seconds being given by $x=a+bt$, $y=c+dt+et^2$, where $a$, $b$, $c$, $d$, $e$ are constants. Show that it moves with uniform acceleration and find meanings for $a$, $b$, $c$, $d$, $e$. If $e=-g$, the acceleration of gravity,... Read More

Question 1 A body travels in a straight line so that the distance $s$ feet travelled in time $t$ seconds from a fixed point in the line of motion is shown by the following equation :- $$s=5.5+17.5t-5t^2$$. Show that the body is travelling with uniform acceleration, find the value of the acceleration, and calculate the... Read More

Question 1 A body of mass $10$ units moves in a straight line so that its distance $s$ from a fixed point in the line of motion at time $t$ is given by the equation : $s=a+bt+ct^2$. Derive formulae for its velocity, acceleration and momentum at any time. Given that when $t=0$ the velocity, acceleration... Read More

Question 1 A wheel rolls uniformly on the ground, without sliding, its centre describing a straight line with uniform velocity $v$. Show that at any instant every point on the rim is turning about the point of contact of the wheel with the ground with an angular velocity equal to that of the wheel about... Read More

Question 1 A particle moves along a straight line and its distance in feet $s$ from a fixed point in the line is given by the formula $s=at^3+bt^2+ct$ where $a$, $b$, $c$ are constants and $t$ denotes the time in seconds. The distance is $16$ when $t=1$ and the velocity is zero when $t=2$ and... Read More