Answer:
The distance by the ball clear the crossbar is 1.15 m
Explanation:
Given that,
Distance = 44 m
Speed = 24 m/s
Angle = 31°
Height = 3.05 m
We need to calculate the horizontal velocity
Using formula of horizontal velocity
[tex]u_{x}=u\cos\theta[/tex]
Put the value into the formula
[tex]u_{x}=24\cos(31)[/tex]
[tex]u_{x}=20.5\ m/s[/tex]
We need to calculate the vertical velocity
Using formula of vertical velocity
[tex]u_{y}=u\sin\theta[/tex]
Put the value into the formula
[tex]u_{y}=24\sin(31)[/tex]
[tex]u_{y}=12.3\ m/s[/tex]
We need to calculate the time
Using formula of time
[tex]t=\dfrac{d}{u_{x}}[/tex]
Put the value into the formula
[tex]t=\dfrac{44}{20.5}[/tex]
[tex]t=2.1\ sec[/tex]
We need to calculate the vertical height
Using equation of motion
[tex]h=u_{y}t+\dfrac{1}{2}at^2[/tex]
Put the value into the formula
[tex]h=12.3\times2.1-\dfrac{1}{2}\times9.8\times(2.1)^2[/tex]
[tex]h=4.2\ m[/tex]
We need to calculate the distance by the ball clear the crossbar
Using formula for vertical distance
[tex]d=h-3.05[/tex]
Put the value of h
[tex]d=4.2-3.05[/tex]
[tex]d=1.15\ m[/tex]
Hence, The distance by the ball clear the crossbar is 1.15 m
