A ball is released from a hot air balloon moving downward with a velocity of
-10.0 meters/second and a height of 1,000 meters. How long did it take the ball to reach the surface of Earth? Given: g = -9.8 meters/second2.
hf=hi+vi*t+1/2 a t^2
0=1000-10t-4.9t^2
solve the quadratic
t=(-10+-sqrt(100+19600))/-9.8
t=-150/-9.8=15.3sec
check that.
incorrect
To find the time it takes for the ball to reach the surface of the Earth, we can use the equation of motion:
h = ut + 1/2 * gt^2
Where:
h = height of the balloon (1,000 meters)
u = initial velocity of the ball (-10.0 meters/second)
g = acceleration due to gravity (-9.8 meters/second^2)
t = time
Since the ball is moving downward, the initial velocity (u) will be negative.
Substituting the given values into the equation, we have:
1,000 = -10t + 1/2 * (-9.8) * t^2
Simplifying the equation, we get:
1,000 = -10t - 4.9t^2
To solve for t, we rearrange the equation to make it equal to zero:
4.9t^2 + 10t - 1,000 = 0
Now, we can use the quadratic formula to find the values of t:
t = (-b ± √(b^2 - 4ac)) / 2a
In this equation, a = 4.9, b = 10, and c = -1,000.
t = (-10 ± √(10^2 - 4 * 4.9 * -1,000)) / (2 * 4.9)
Calculating further:
t = (-10 ± √(100 + 19,600)) / 9.8
t = (-10 ± √19,700) / 9.8
Using a calculator to evaluate, we get two solutions: t ≈ 10.06 seconds and t ≈ -203.02 seconds. Since time cannot be negative in this case, we ignore the negative solution.
Therefore, the ball takes approximately 10.06 seconds to reach the surface of the Earth.