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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After they fall?
To write the functions for the height of each ball, we can use the formula for the height of an object dropped from a certain height under the influence of gravity. The formula is:
h(t) = h0 - (1/2) * g * t^2
Where:
- h(t) represents the height of the object at time t
- h0 is the initial height of the object
- g is the acceleration due to gravity (which is approximately 32.2 ft/s^2)
- t is the time elapsed
Using this formula, we can write the functions for the height of each ball:
h1(t) = 100 - (1/2) * 32.2 * t^2
h2(t) = 210 - (1/2) * 32.2 * t^2
To find when each ball reaches the ground, we can set h(t) equal to 0 and solve for t:
For ball 1:
0 = 100 - (1/2) * 32.2 * t^2
Simplifying the equation, we get:
50 * t^2 = 100
Dividing by 50:
t^2 = 2
Taking the square root of both sides:
t = √2
For ball 2:
0 = 210 - (1/2) * 32.2 * t^2
Simplifying the equation, we get:
16.1 * t^2 = 210
Dividing by 16.1:
t^2 = 13.04
Taking the square root of both sides:
t = √13.04
Rounded to the nearest hundredth:
Ball 1 reaches the ground at approximately 1.41 seconds.
Ball 2 reaches the ground at approximately 3.61 seconds.