A soccer ball is kicked off of the ground at 17 ft/sec @ 30 degrees. Determine the maximum height above the ground the ball reaches and how far downfield the ball lands.
time in the air...
hf=hi+vi*t-1/2 gt^2
0=0+17 sin30 t -4.9t^2 solve for time in air t.
max height? figure max height is at t/2
hf=vi*t/2 - 4/9 (t/2)^2
distance?
d=vhoriz*t where vhoriz=17*cos30
To determine the maximum height above the ground the soccer ball reaches and how far downfield it lands, we can use the equations of motion for projectile motion.
Given:
Initial velocity (vi) = 17 ft/sec
Launch angle (θ) = 30 degrees
Let's break down the problem into two components: vertical and horizontal.
Vertical Component:
To find the maximum height (h), we can use the following equation:
h = (vi^2 * sin^2(θ)) / (2 * g)
where g is the acceleration due to gravity (approximately 32.2 ft/sec^2).
Plugging in the given values:
h = (17^2 * sin^2(30)) / (2 * 32.2)
Evaluate the equation to find the maximum height, h.
Horizontal Component:
To find how far downfield the ball lands (range), we can use the following equation:
range = (vi^2 * sin(2θ)) / g
Plugging in the given values:
range = (17^2 * sin(2 * 30)) / 32.2
Evaluate the equation to find the range.
So, by using these equations, you can determine the maximum height above the ground the soccer ball reaches and how far downfield it lands.