An object is taken from point P to point R either by a direct route or by the route P to Q to R, as shown in Fig. 3.1. P and Q are on the same horizontal level. R is vertically above Q. Explain whether the work done moving the object against the gravitational field is the same or different along paths PR and PQR.
A ball is projected with initial velocity $V$ at an angle $\theta$ to the horizontal, as shown in Fig. 3.2. The graph in Fig. 3.3 shows how the height $h$ of the ball varies with time $t$. Air resistance is negligible. Use the time for the ball to reach its greatest height to find the vertical component $V_v$ of the velocity of the ball at $t = 0$.
The ball’s horizontal displacement at $t = 3.00\,\text{s}$ is $25.5\,\text{m}$. On Fig. 3.4, sketch the variation with $t$ of the ball’s horizontal displacement $x$.
For the ball at maximum height, calculate the ratio $\frac{\text{potential energy of the ball}}{\text{kinetic energy of the ball}}$.
In practice, air resistance is not negligible. State and explain how air resistance affects the time the ball takes to reach its maximum height.