Answer:
(1). This motion is projectile motion.
(2). The horizontal initial velocity is 19.3 m/s.
The vertical initial velocity is 22.9 m/s.
(3). The time is 3.9 sec.
(4). The range of the ball assuming the ground is flat and horizontal is 90.4 m.
Explanation:
Given that,
Angle = 40°
Velocity = 30 m/s
(1). A soccer ball is kicked at an angle from the ground at a speed of 30 m/s.
So, this motion will be projectile motion.
(2). We need to calculate the vertical and horizontal components of the initial velocity of the ball
Using formula of vertical initial velocity
[tex]u_{y}=u\cos\theta[/tex]
Put the value into the formula
[tex]u_{y}=30\cos40[/tex]
[tex]u_{y}=22.9\ m/s[/tex]
Horizontal initial velocity ,
[tex]u_{x}=u\sin\theta[/tex]
Put the value into the formula
[tex]u_{x}=30\sin40[/tex]
[tex]u_{x}=19.3\ m/s[/tex]
(3). We need to calculate the time
Using formula of time
[tex]t=\dfrac{2u\sin\theta}{g}[/tex]
Put the value into the formula
[tex]t=\dfrac{2\times19.3}{9.8}[/tex]
[tex]t=3.9\ sec[/tex]
(4). We need to calculate the range of the ball assuming the ground is flat and horizontal
Using formula of range
[tex]R=\dfrac{v^2\sin2\theta}{g}[/tex]
Put the value into the formula
[tex]R=\dfrac{30^2\sin80}{9.8}[/tex]
[tex]R=90.4\ m[/tex]
Hence, (1). This motion is projectile motion.
(2). The horizontal initial velocity is 19.3 m/s.
The vertical initial velocity is 22.9 m/s.
(3). The time is 3.9 sec.
(4). The range of the ball assuming the ground is flat and horizontal is 90.4 m.
