Martina hits volley ball with an upward velosity of 13
M/s 1meterabove the grund. How long will it take for the ball to hit the ground.
Vi = 13 m/s
Hi = 1.0 m
h = Hi + Vi t - 4.9 t^2
0 = 1 + 13 t - 4.9 t^2
now it is algebra
4.9 t^2 - 13 t - 1 = 0
t = [ 13 +/- sqrt (169 + 19.6)/9.81
use positive time :)
t = 2.73 seconds
(good hit, wow ! )
To determine the time it takes for the volleyball to hit the ground, we need to use the kinematic equation for vertical motion:
Δy = v₀t + (1/2)at²
Where:
Δy is the change in height (which is -1 meter, since the ball is 1 meter above the ground),
v₀ is the initial upward velocity (which is 13 m/s),
t is the time, and
a is the acceleration due to gravity (-9.8 m/s²).
Since we are looking for the time it takes for the ball to hit the ground, we can rearrange the equation to solve for t:
-1 = (13)t + (1/2)(-9.8)t²
Simplifying the equation, we can write it as a quadratic equation:
-4.9t² + 13t - 1 = 0
To solve for t, we can use the quadratic formula:
t = (-b ± √(b² - 4ac)) / 2a
Plugging in the values, we have:
a = -4.9
b = 13
c = -1
t = (-(13) ± √((13)² - 4(-4.9)(-1))) / (2(-4.9))
After simplification, we can calculate the two potential solutions for t. However, since we are looking for the time it takes for the ball to hit the ground, we only consider the positive root of the equation:
t ≈ 1.07 seconds
Therefore, it will take approximately 1.07 seconds for the volleyball to hit the ground.