Question
A baseball is hit upward with velocity of 40 ft per second ignoring the height of the baseball player how long does it take for the ball to fall to the ground use the formula h(t) = v0t-16t^2 where h(t) is the height of an object in feet v0 is the object's initial velocity in feet per second and t is the time in seconds
Answers
GPT-4o mini
To determine how long it takes for the baseball to hit the ground, we can use the formula you provided:
\[
h(t) = v_0 t - 16 t^2
\]
In this case, the initial velocity \(v_0\) is 40 ft/s. Therefore, the equation becomes:
\[
h(t) = 40t - 16t^2
\]
We need to find the time \(t\) when the ball hits the ground, which means setting \(h(t)\) equal to 0:
\[
0 = 40t - 16t^2
\]
Rearranging this equation gives:
\[
16t^2 - 40t = 0
\]
Now, we can factor out \(t\):
\[
t(16t - 40) = 0
\]
This gives us two solutions:
1. \(t = 0\) (the time at which the ball is hit)
2. \(16t - 40 = 0\)
Now, solving \(16t - 40 = 0\):
\[
16t = 40
\]
\[
t = \frac{40}{16} = \frac{5}{2} = 2.5 \text{ seconds}
\]
Thus, the baseball takes **2.5 seconds to hit the ground** after it is struck.
\[
h(t) = v_0 t - 16 t^2
\]
In this case, the initial velocity \(v_0\) is 40 ft/s. Therefore, the equation becomes:
\[
h(t) = 40t - 16t^2
\]
We need to find the time \(t\) when the ball hits the ground, which means setting \(h(t)\) equal to 0:
\[
0 = 40t - 16t^2
\]
Rearranging this equation gives:
\[
16t^2 - 40t = 0
\]
Now, we can factor out \(t\):
\[
t(16t - 40) = 0
\]
This gives us two solutions:
1. \(t = 0\) (the time at which the ball is hit)
2. \(16t - 40 = 0\)
Now, solving \(16t - 40 = 0\):
\[
16t = 40
\]
\[
t = \frac{40}{16} = \frac{5}{2} = 2.5 \text{ seconds}
\]
Thus, the baseball takes **2.5 seconds to hit the ground** after it is struck.