Question

question 5
choose the best answer from the options that follow each question.
a volleyball player taps a volleyball well above the net. the balls speed is least
when the horizontal and vertical components of its velocity are equal.
just after it is tapped by the player.
just before it strikes the ground.
at the highest point of its path.
question 6
choose the best answer from the options that follow each question.
a gardener holds the nozzle of a hose constant at a small angle above the horizontal and observes the path of the stream of water coming from the nozzle. if the pressure of the water is increased so that the water leaves the nozzle at a greater speed,
the height of the waters path will increase but the width of the path will remain the same.
the height and width of the waters path will increase.
the height and width of the waters path will remain the same.
the width of the waters path will increase but the height will remain the same.

Explanation:

Step1: Analyze volleyball motion

The motion of the volleyball is a projectile - motion. The speed of a projectile \(v = \sqrt{v_x^2 + v_y^2}\), where \(v_x\) is the horizontal component of velocity and \(v_y\) is the vertical component of velocity. In projectile - motion, the horizontal component of velocity \(v_x\) remains constant (neglecting air - resistance), and the vertical component \(v_y\) changes due to gravity. At the highest point of its path, \(v_y = 0\), so the speed \(v=v_x\), which is the minimum speed during the motion.

Step2: Analyze water - stream motion

For the water coming out of the hose, the motion is also a projectile - motion. The maximum height of a projectile \(H=\frac{v_0^2\sin^2\theta}{2g}\) and the range \(R=\frac{v_0^2\sin2\theta}{g}\), where \(v_0\) is the initial velocity, \(\theta\) is the angle of projection, and \(g\) is the acceleration due to gravity. When the initial speed \(v_0\) of the water increases, both \(H\) and \(R\) increase because \(H\propto v_0^2\) and \(R\propto v_0^2\).

Answer:

Question 5: at the highest point of its path.
Question 6: the height and width of the water’s path will increase.