Calculate how long the ball takes to get to the ground.
Calculate the vertical velocity component of the ball when it reaches the ground.
Determine the magnitude and the angle to the horizontal of the velocity of the ball as it hits the ground.
The ball is launched by a compressed spring attached to a fixed block, as shown in Fig. 2.2. The ball is positioned on a frictionless track in front of the spring. It is then pulled back so that the spring has compression $x_0$. When the spring is released, the ball is projected horizontally as shown in Fig. 2.3.
The ball is a uniform sphere of steel of diameter $0.016\,\text{m}$ and mass $0.017\,\text{kg}$. Calculate the density of the steel.
Every bit of the elastic potential energy in the spring becomes kinetic energy of the ball. The ball leaves the spring at a speed of $4.9\,\text{m s}^{-1}$. Show that the maximum elastic potential energy of the spring is $0.20\,\text{J}$.
Use Fig. 2.4 to determine the spring constant $k$ of the spring.
Use your answer in (b)(iii) together with the energy from (b)(ii) to find the compression $x_0$ of the spring.
The steel ball is swapped for a polystyrene ball with the same diameter but a much smaller mass. The spring is compressed by $x_0$ and then released. Air resistance on this ball is not negligible after it leaves the spring. Explain why this ball leaves the spring with a greater speed than that of the steel ball.
Explain why this ball takes a longer time to reach the ground than the steel ball.