Martina hits a volleyball with a velosity of 13 m^s. When she hits the ball it is 1m above the ground. How long will ot take for the ball to hit the ground.
see problem below this one.
http://www.jiskha.com/display.cgi?id=1452879533#1452879533.1452880085
To find the time it takes for the ball to hit the ground, we can use a physics equation known as the kinematic equation. Specifically, we can use the equation for vertical motion:
h = ut + (1/2)gt^2
Where:
h = height (in this case, the initial height of the ball above the ground)
u = initial velocity (the velocity at which Martina hits the ball)
g = acceleration due to gravity (approximately 9.8 m/s^2)
t = time
In this case, the initial height (h) is 1 meter, the initial velocity (u) is 13 m/s, and the acceleration due to gravity (g) is -9.8 m/s^2 (negative because it acts downwards). We need to solve for t.
Rearranging the equation, we have:
0 = (1/2)(-9.8)t^2 + 13t - 1
This is a quadratic equation. We can solve it by factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula to find the time it takes for the ball to hit the ground:
t = (-b ± √(b^2 - 4ac))/(2a)
For this equation, a = (1/2)(-9.8), b = 13, and c = -1.
Substituting the values into the quadratic formula, we have:
t = (-(13) ± √((13)^2 - 4((1/2)(-9.8))(-1))) / (2((1/2)(-9.8)))
Simplifying further:
t = (-13 ± √(169 + 19.6)) / (-9.8)
Now, calculate the values within the square root:
t = (-13 ± √(188.6)) / (-9.8)
Using a calculator, we find:
t ≈ (-13 ± 13.73) / (-9.8)
There are two possible solutions for t:
t ≈ (-13 + 13.73) / (-9.8) ≈ 0.071 seconds
t ≈ (-13 - 13.73) / (-9.8) ≈ 2.285 seconds
Since time cannot be negative in this context, the ball takes approximately 2.285 seconds to hit the ground.