Free Fall:
Tara throws a baseball down to Nathan. If she throws it with a speed of 2.0m/s and it lands in Nathan's hand with a speed of 10.0m/s, how far above Nathan is Tara?
V^2 = Vo^2 + 2gd,
10^2 = 2^2 + 2*9.8*d,
100 = 4 + 19.6d,
100 - 4 = 19.6d,
96 = 19.6d,
d = 96/19.6 = 4.9 m.
VF^2=Vi^2+2gx
10^2=2^2+2(9.8)x
96=19.6x
x=4.9m
To find the distance above Nathan that Tara is when she throws the baseball, we need to calculate the height (vertical distance) that the baseball traveled during its free fall.
We can start by using the equation of motion for free fall:
v² = u² + 2as
Where:
v = final velocity (10.0 m/s)
u = initial velocity (2.0 m/s)
a = acceleration due to gravity (-9.8 m/s²) since the baseball is falling
s = distance traveled
Rearranging the equation to solve for s:
s = (v² - u²) / (2a)
Substituting the given values:
s = (10.0² - 2.0²) / (2 * -9.8)
Calculating the numerator:
s = (100 - 4) / (2 * -9.8)
s = 96 / -19.6
Calculating the value of s:
s = -4.898 meters
The negative sign indicates that the distance s is in the downward direction.
Therefore, Tara is approximately 4.898 meters above Nathan when she throws the baseball.