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

h1(t) = 100 - 0.5*32*t^2.

h1 = 100 - 16t^2 = 0 @ gnd. level.
16t^2 = 100
t^2 = 6.25
t = 2.50 s.

h2(t) = 210 - 0.5*32*t^2

h2 = 210 - 16t^2 = 0 @ gnd. level.
16t^2 = 210
t^2 = 13.125
t = 3.62 s.

To write the functions for the height of each ball, we can use the equation for free fall:

h(t) = h0 + v0t - (1/2)gt^2

where:
- h(t) is the height of the ball at time t,
- h0 is the initial height of the ball,
- v0 is the initial velocity of the ball (which is 0 in this case because the ball is dropped without any initial velocity),
- g is the acceleration due to gravity (approximately 32.2 ft/s^2).

For ball 1:
- h0 = 100 ft
- v0 = 0 ft/s
- g = 32.2 ft/s^2

So the function for the height of ball 1 would be:
h1(t) = 100 - (1/2) * 32.2 * t^2

For ball 2:
- h0 = 210 ft
- v0 = 0 ft/s
- g = 32.2 ft/s^2

So the function for the height of ball 2 would be:
h2(t) = 210 - (1/2) * 32.2 * t^2

To find when each ball reaches the ground, we need to find the time when the height is 0. We can set h(t) = 0 in each equation and solve for t.

For ball 1:
0 = 100 - (1/2) * 32.2 * t^2
Solving this equation will give us the time when ball 1 reaches the ground.

For ball 2:
0 = 210 - (1/2) * 32.2 * t^2
Solving this equation will give us the time when ball 2 reaches the ground.

Let's solve these equations to find the answers.