Stephanie hits a volleyball from a height of 0.80m and gives it on initial velocity of 17.5m/s straight up

1. How high will the volleyball go?
2.how long will it take the ball to reach its maximum height?

To solve these questions, we can use the equations of motion for projectile motion. Let's break down each question:

1. How high will the volleyball go?
To determine the maximum height reached by the volleyball, we can use the equation for vertical displacement in projectile motion. The equation is:

h = h0 + (v0^2 * sin^2(theta)) / (2 * g)

Where:
h = maximum height reached
h0 = initial height (0.80m)
v0 = initial velocity (17.5m/s)
theta = angle of projection (since it's straight up, theta = 90°)
g = acceleration due to gravity (usually taken as 9.8m/s^2)

Plugging in the values into the equation:

h = 0.80 + (17.5^2 * sin^2(90°)) / (2 * 9.8)

Since sin 90° = 1, the equation simplifies to:

h = 0.80 + (17.5^2) / (2 * 9.8)

Calculating this gives us the maximum height the volleyball will reach.

2. How long will it take the ball to reach its maximum height?
To find the time it takes for the volleyball to reach its maximum height, we can use the equation for time of flight. The equation is:

t_flight = (v0 * sin(theta)) / g

Again, since the ball is moving straight up, theta = 90°, so the equation simplifies to:

t_flight = (v0 * sin(90°)) / g

Since sin 90° = 1, the equation further simplifies to:

t_flight = v0 / g

Plugging in the values:

t_flight = 17.5 / 9.8

Calculating this gives us the time it takes for the volleyball to reach its maximum height.

To determine the answers, we can use equations of motion for projectile motion.

1. How high will the volleyball go?
To find the maximum height reached by the volleyball, we can use the equation:

vf^2 = vi^2 + 2ad

Where:
vf = final velocity (0 m/s at maximum height, as the ball changes direction)
vi = initial velocity (17.5 m/s)
a = acceleration (assumed to be the acceleration due to gravity, -9.8 m/s^2)
d = vertical displacement or height

Rearranging the equation, we get:

d = (vf^2 - vi^2) / (2a)

Substituting the values, we have:

d = (0 - 17.5^2) / (2 * -9.8)

d = -306.25 / -19.6

d = 15.63 meters

Therefore, the volleyball will go up to a height of approximately 15.63 meters.

2. How long will it take the ball to reach its maximum height?
To find the time taken to reach the maximum height, we can use the equation:

vf = vi + at

At maximum height, the final velocity is 0 m/s, and the acceleration (a) is -9.8 m/s^2 (due to gravity acting against the upward motion of the ball). The initial velocity (vi) is 17.5 m/s.

Rearranging the equation, we have:

0 = 17.5 - 9.8t

9.8t = 17.5

t = 17.5 / 9.8

t ≈ 1.79 seconds

Therefore, it will take approximately 1.79 seconds for the volleyball to reach its maximum height.