Veronica hits a volleyball from a height of 0.4 m and gives it an initial velocity of 5.2 m/s straight up.
a) How high, above the ground, will the volleyball go
b) How long will it take the ball to reach its maximum height?
At the top, v=0
vf=vi+at
0=5.2-9.8t
solve for t.
Now, at that time
hf=hi+vi*t-4.9t^2
hf=.4+5.2t-4.9t^2 put t in, and solve for final height hf
To find the answers to these questions, we can use concepts from the laws of motion, specifically applying them to the motion of the volleyball. We can use the equations of motion and kinematics to solve for the required quantities.
a) To determine how high the volleyball will go above the ground, we need to calculate the maximum height it will reach. At the maximum height, the vertical velocity will be zero.
1. Identify the known quantities:
- Initial velocity (u) = 5.2 m/s (upwards)
- Final velocity (v) = 0 m/s (at maximum height)
- Acceleration (a) = -9.8 m/s² (due to gravity, acting downwards)
- Displacement (s) = ? (height above the ground, what we need to find)
2. Use the kinematic equation to solve for the displacement:
v² = u² + 2as
Plugging in the values:
0² = (5.2)² + 2(-9.8)s
Simplifying:
0 = 27.04 - 19.6s
Rearrange the equation:
19.6s = 27.04
Solve for s:
s = 27.04 / 19.6 ≈ 1.38 m
Therefore, the volleyball will reach a height of approximately 1.38 m above the ground.
b) Now, let's determine the time it takes for the ball to reach its maximum height. We can use the equation of motion involving time:
3. Use the equation to solve for time (t):
v = u + at
Plugging in the values:
0 = 5.2 + (-9.8)t
Rearrange and solve for t:
9.8t = 5.2
t = 5.2 / 9.8 ≈ 0.53 s
Therefore, it will take approximately 0.53 seconds for the volleyball to reach its maximum height.