Two identical rubber balls are dropped from different heights. Ball 1 is dropped from a height of 100 feet, and ball 2 is dropped from a height of 210 feet. Write a function for the height of each ball.
h1(t) =
h2(t) =
When does ball 1 reach the ground? Round to the nearest hundredth. _____seconds
When does ball 2 reach the ground? Round to the nearest hundredth. _____seconds
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To write a function for the height of each ball, we can use the formula for the height of an object in free fall:
h(t) = h0 - 0.5*g*t^2
Where:
- h(t) is the height of the object at time t
- h0 is the initial height of the object
- g is the acceleration due to gravity (approximately -32.2 ft/s^2)
- t is the time in seconds
For ball 1:
h1(t) = 100 - 0.5*32.2*t^2
For ball 2:
h2(t) = 210 - 0.5*32.2*t^2
To find when each ball reaches the ground, we can set the height (h) to zero and solve for t.
For ball 1:
100 - 0.5*32.2*t^2 = 0
Simplifying the equation:
-0.5*32.2*t^2 = -100
Solving for t:
t^2 = (-100) / (-0.5*32.2)
t^2 = 100 / 16.1
t^2 = 6.21118
t = sqrt(6.21118)
t ≈ 2.49 seconds
Ball 1 reaches the ground approximately 2.49 seconds after being dropped.
For ball 2:
210 - 0.5*32.2*t^2 = 0
Simplifying the equation:
-0.5*32.2*t^2 = -210
Solving for t:
t^2 = (-210) / (-0.5*32.2)
t^2 = 210 / 16.1
t^2 = 13.04348
t = sqrt(13.04348)
t ≈ 3.61 seconds
Ball 2 reaches the ground approximately 3.61 seconds after being dropped.