A beach ball, moving with a speed of +1.28 m/s rolls off a pier and hits the water a horizontal distance of 0.74 m from the end of the pier. How high (magnitude only) above the water is the pie?

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32 To find the height of the pier above the water, we can make use of the horizontal distance the beach ball traveled.

We can use the equation for horizontal motion:

Horizontal Distance = Horizontal Velocity × Time

Since the initial velocity (u) is 0 m/s (the ball rolls off the pier), and the final velocity (v) is 1.28 m/s (given), we can rearrange the equation to solve for time:

Time = Horizontal Distance / Horizontal Velocity

Substituting the given values:

Time = 0.74 m / 1.28 m/s

Calculating the time:

Time = 0.57 s

Now, we can analyze the vertical motion of the beach ball.

Using the equations of motion, we can find the vertical displacement (the height above the water) of the pier. Since the ball rolls off the pier, the initial vertical velocity (u) is 0 m/s. The acceleration due to gravity (g) is approximately 9.8 m/s², and the time (t) is 0.57 s (as calculated above).

We can use the equation:

Vertical Displacement = (Initial Vertical Velocity × Time) + (0.5 × Acceleration × Time²)

Since the initial velocity (u) is 0 m/s, the equation simplifies to:

Vertical Displacement = 0.5 × Acceleration × Time²

Substituting the values:

Vertical Displacement = 0.5 × 9.8 m/s² × (0.57 s)²

Calculating the vertical displacement:

Vertical Displacement = 1.84 m

Therefore, the magnitude of the height of the pier above the water is 1.84 meters.