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
his is quite similar to the rocket problem. You should know the equation for height of a projectile. Just use it to solve for t when the height is zero.
How far do you get? Where do you get stuck? "I have no idea" is not a useful attempt at a solution.
To find the function for the height of each ball, we can use the equation for free fall:
h(t) = 0.5 * g * t^2 + v0 * t + h0
Where:
h(t) is the height of the ball at time t
g is the acceleration due to gravity (approximately -32.2 ft/s^2)
t is the time in seconds
v0 is the initial velocity of the ball
h0 is the initial height of the ball
For ball 1, the initial height is 100 feet and the initial velocity is 0, so the equation becomes:
h1(t) = 0.5 * (-32.2) * t^2 + 0 * t + 100
Simplifying:
h1(t) = -16.1 * t^2 + 100
For ball 2, the initial height is 210 feet and the initial velocity is 0, so the equation becomes:
h2(t) = 0.5 * (-32.2) * t^2 + 0 * t + 210
Simplifying:
h2(t) = -16.1 * t^2 + 210
To find when each ball reaches the ground, we can set h(t) equal to 0 and solve for t. In other words, we want to find the time when the height of the ball is 0.
For ball 1:
-16.1 * t^2 + 100 = 0
Solving this quadratic equation, we get two solutions:
t = 0 or t = 6.21
Rounding to the nearest hundredth, ball 1 reaches the ground at approximately 6.21 seconds.
For ball 2:
-16.1 * t^2 + 210 = 0
Again, solving this quadratic equation, we get two solutions:
t = 0 or t = 9.13
Rounding to the nearest hundredth, ball 2 reaches the ground at approximately 9.13 seconds.