Answer:
0.72secs
Step-by-step explanation:
Given the height of the ball in air modeled by the equation:
h=−16t²+23t+4
Required
Total time it spent in the air
To get this we need to calculate its time at the maximum height
At the maximum height,
v = dh/dt = 0
-32t + 23 = 0
-32t = -23
t = 23/32
t = 0.72secs
Hence the total time it spend in the air will be 0.72secs
The total time for which the ball is in the air is 0.72 seconds and this can be determined by differentiating the given function.
Given :
A boy throws a ball into the air. The equation [tex]\rm h = -16t^2+23t+4[/tex] models the path of the ball, where h is the height (in feet) of the ball t seconds after it is thrown.
Differentiate the given function of height with respect to 't' in order to determine the value of 't'.
[tex]\rm h = -16t^2+23t+4[/tex]
[tex]\rm \dfrac{dh}{dt}=-32t+23[/tex]
Now, equate the above differential equation to zero.
-32t + 23 = 0
23 = 32t
t = 0.72 seconds
So, the total time for which the ball is in the air is 0.72 seconds.
For more information, refer to the link given below:
https://brainly.com/question/24062595
