Respuesta :
Answer:
The ball travel horizontally before it hit the ground is 34.22 feet.
Step-by-step explanation:
Given that,
Height = 3 feet
Angle = 24 °
Initial velocity = 110 feet/s
We need to write a parametric equation for the flight of the ball
Using given data
[tex]r(t)=u\cos\theta\times t\hat{i}+(h+(u\sin\theta)t-\dfrac{1}{2}gt^2)\hat{j}[/tex]
Put the value into the formula
[tex]r(t)=110\cos24\times t\ i+(3+110\sin24\times t-\dfrac{1}{2}32t^2)j[/tex]
[tex]r(t)=100.4t(i)+(3+44.7t-16t^2)j[/tex]
Now, on differentiating w.r.to t
[tex]v(t)=100.4i+(44.7-32t)j[/tex]....(I)
We need to calculate the time
Using equation (I)
If y'(t)=0, then the ball will be at maximum height
So, [tex]y'(t)=44.7-32t[/tex]
Put the value of y'(t)
[tex]44.7-32t=0[/tex]
[tex]t=\dfrac{44.7}{32}[/tex]
[tex]t=1.4\ sec[/tex]
We need to calculate the maximum height
Using equation of motion
[tex]y(t)=h+ut-\dfrac{1}{2}gt^2[/tex]
Put the value into the formula
[tex]y(1.4)=3+44.7\times1.4-16\times(1.4)^2[/tex]
[tex]y(1.4)=34.22\ feet[/tex]
Hence, The ball travel horizontally before it hit the ground is 34.22 feet.
