Stephanie hits a volleyball from a height of 0.80 m and gives it an initial velocity of 7.5 m/s straight up.

a) how high will the volleyball go?
b) how long will it take the ball to reach its maximum height? ( Hint: At maximum height, v = 0 m/s)

a) 2.78 m

b) .765 s

a) Well, volleyball that goes all the way into the sky... that's called a "sky-ball"! Haha! But seriously, let's calculate how high this sky-ball will go. We can use the equation for vertical motion: Δy = v₀² / (2g).

Given that the initial velocity, v₀, is 7.5 m/s and the acceleration due to gravity, g, is approximately 9.8 m/s², we can plug in the numbers:

Δy = (7.5 m/s)² / (2 * 9.8 m/s²)

Calculating that, you get:

Δy ≈ 2.87 m

So, the volleyball will go approximately 2.87 meters high. That's quite a leap!

b) Now, to find out how long it takes for the ball to reach its maximum height, we can use another equation for vertical motion: v = v₀ - gt. At maximum height, v is 0 m/s.

So, let's set up the equation:

0 = 7.5 m/s - 9.8 m/s² * t

Solving for t, we have:

t ≈ 7.5 m/s / (9.8 m/s²)

Calculating that, you get:

t ≈ 0.76 s

So, it will take about 0.76 seconds for the ball to reach its maximum height. That's quicker than a sneeze! God bless you!

To solve these questions, we can use the equations of motion for vertical motion.

a) To find the maximum height the volleyball will reach, we can use the equation for displacement in vertical motion:

Δy = v₀y * t - 0.5 * g * t²

Where:
Δy is the displacement (change in height)
v₀y is the initial vertical velocity
t is the time taken
g is the acceleration due to gravity (approximately 9.8 m/s²)

In this case, the initial velocity (v₀y) is 7.5 m/s straight up, and we need to find the maximum height. At the maximum height, the vertical velocity is 0 m/s. Therefore, we can set v₀y to 0 in the equation:

Δy = 0 * t - 0.5 * g * t²
Δy = -0.5 * g * t²

The displacement (Δy) will be equal to the maximum height the volleyball reaches. So, we need to solve for Δy.

b) To find the time taken for the ball to reach its maximum height, we can use the equation for vertical velocity:

v = v₀y - g * t

At the maximum height, the vertical velocity (v) is 0 m/s. Therefore, we can set v to 0 in the equation:

0 = 7.5 - 9.8 * t

Now, we can solve this equation to find the time taken for the ball to reach its maximum height.

I hope this explanation helps you understand how to solve these types of questions! If you have any specific values for the acceleration due to gravity or any other missing data, please provide them so I can help you with the calculations.

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