Question

pretest: unit 5
a water - skier with a mass of 68 kg is pulled with a constant force of 980 n by a speedboat. a wave launches him in such a way that he is temporarily airborne while still being pulled by the boat, as shown in the image below. assuming that air resistance can be ignored, what is the vertical acceleration that the water - skier experiences on his return to the water surface? (recall that g = 9.8 m/s²)
rope force 980 n
35.0°
weight
a. -9.8 m/s²
b. -11.2 m/s²
c. -15.6 m/s²
d. -18.1 m/s²

Explanation:

Step1: Analyze vertical forces

The only vertical - acting force on the water - skier when in the air (ignoring air resistance) is the force of gravity. According to Newton's second law, the net force in the vertical direction $F_{net,y}=ma_y$. The force of gravity is given by $F_g = mg$, where $m$ is the mass of the water - skier and $g$ is the acceleration due to gravity. The direction of the force of gravity is downward, so the net force in the vertical direction is $F_{net,y}=-mg$.

Step2: Calculate vertical acceleration

From Newton's second law $F_{net,y}=ma_y$, and since $F_{net,y}=-mg$, we can solve for $a_y$. Dividing both sides of the equation $-mg = ma_y$ by $m$ (where $m
eq0$), we get $a_y=-g$. Given that $g = 9.8\ m/s^2$, then $a_y=-9.8\ m/s^2$.

Answer:

A. $-9.8\ m/s^2$