Stephanie serves a volleyball from a height of 0.76 m and gives it an initial velocity of +7.2m/s straight up.How high will the volleyball go? The acceleration of gravity is 9.81 m/s2.
Answer in units of m.
2) How long will it take the ball to reach its maximum height? Answer in units of s.
vi^2=mgh where h is the height above .76m, so add that to h.
how long? when you find the h(before you add)
h=vi*t-4.9t^2 solve for t.
52.6
1.88
To solve these two problems, we can use the equations of motion and kinematics. Let's tackle each problem separately:
1) How high will the volleyball go?
To find the maximum height reached by the volleyball, we need to determine the final height. We know the initial velocity of the volleyball (7.2 m/s), the acceleration due to gravity (-9.81 m/s²), and the initial height (0.76 m). We can use the kinematic equation:
vf² = vi² + 2ad
Here, vf represents the final velocity, vi is the initial velocity, a is the acceleration, and d is the displacement. Since we want to find the maximum height, vf will be zero since the ball reaches its highest point there. We can rearrange the equation to solve for d:
0 = (7.2 m/s)² + 2(-9.81 m/s²)d
This simplifies to:
0 = 51.84 m²/s² - 19.62 m/s² d
Rearranging again:
d = (51.84 m²/s²) / (19.62 m/s²)
Calculating this gives us:
d ≈ 2.64 m
Therefore, the volleyball will reach a height of approximately 2.64 meters.
2) How long will it take the ball to reach its maximum height?
To find the time it takes for the ball to reach its maximum height, we can use the formula:
vf = vi + at
Here, vf represents the final velocity (which is zero at the maximum height), vi is the initial velocity (7.2 m/s), a is the acceleration (-9.81 m/s²), and t is the time we want to find. Rearranging the equation gives us:
0 = 7.2 m/s + (-9.81 m/s²)t
Simplifying:
-7.2 m/s = -9.81 m/s²t
Dividing both sides by -9.81 m/s² gives us:
t = (-7.2 m/s) / (-9.81 m/s²)
Calculating this gives us:
t ≈ 0.734 s
Therefore, it will take approximately 0.734 seconds for the ball to reach its maximum height.