stephanie serves a volleyball from a height of .8m and gives it an initial velocity of 7.6m/s straight up. how high will it go? how long will it take to reach maximum height?
YOu can use energy relationships.
Initial energy= final PE
mg*.8+ 1/2 m 7.6^2=mgh
solve for final h.
How long? how long does it take to fall back?
hf=hi-1/2 g t^2
.8=h-4.9 t^2 solve for t, using h above.
To find out how high the volleyball will go and how long it will take to reach its maximum height, we need to use the equations of motion for constant acceleration.
Let's break down the problem and apply the equations step by step:
1. First, we need to determine the acceleration of the volleyball. In this case, the only force acting on the volleyball is gravity, so its acceleration will be the acceleration due to gravity (g). The standard value for acceleration due to gravity is approximately 9.8 m/s².
2. To calculate how high the volleyball will go, we can use the kinematic equation: v² = u² + 2as, where:
- v is the final velocity (0 m/s at the highest point since it momentarily comes to rest),
- u is the initial velocity (7.6 m/s upwards),
- a is the acceleration (-9.8 m/s² downwards due to gravity), and
- s is the distance (height) covered.
Plugging in the known values, we get:
0² = 7.6² + 2(-9.8)s
Solve this equation for s:
0 = 57.76 - 19.6s
19.6s = 57.76
s = 57.76 / 19.6
s ≈ 2.95 meters
Therefore, the volleyball will reach a height of approximately 2.95 meters.
3. To find the time it takes to reach the maximum height, we can use the equation: v = u + at, where:
- v is the final velocity (0 m/s at the highest point),
- u is the initial velocity (7.6 m/s up),
- a is the acceleration (-9.8 m/s² due to gravity), and
- t is the time.
Plugging in the known values, we get:
0 = 7.6 - 9.8t
Solve this equation for t:
9.8t = 7.6
t = 7.6 / 9.8
t ≈ 0.78 seconds
Therefore, it will take approximately 0.78 seconds for the volleyball to reach its maximum height.