Vincent kicks a soccer ball which remains in the air for 4 seconds and lands 40 m down the field. Show that the ball left his foot at a speed of about 22 m per second.
#Projectile Motion 2
fiery pelican
earnest widget
Vincent kicks a soccer ball which remains in the air for 4 seconds and lands 40 ...
is 40 m the height or the horizontal distance from start to landing?
earnest widget
He kicked the ball to reach the hight of 40 m.
but if you use the formula when it's going down:
S = (1/2)gt²
g = 10 m/s²
t = 4/2 = 2 seconds
then:
S = (1/2)×10×2² = 20 m ≠ 40 m
fiery pelican
This is how I did mine. I got the time of flight and used the time of flight formula but it did not work.
You would have to get about 22 m/s as your answer.
earnest widget
Vincent kicks a soccer ball which remains in the air for 4 seconds and lands 40 ...
if 40 m is the horizontal distance:
v cos(a) × 4 = 40
v cos(a) = 10 (1)
v sin(a) - gt = 0
g = 10 m/s²
t = 4/2 = 2 s
v sin(a) - 10×2 = 0
v sin(a) - 20 = 0
v sin(a) = 20 (2)
from (1) and (2) we get:
(v sin(a))/(v cos(a)) = 20/10 = 2
tan(a) = 2 = 2/1 = opp/adj
hyp = sqrt(2²+1²) = sqrt(5)
cos(a) = 1/sqrt(5)
plug it in to (1):
v × (1/sqrt(5)) = 10
v = 10 sqrt(5) ≈ 22.36 m/s
earnest widget
if 40 m is the horizontal distance:
v cos(a) × 4 = 40
v cos(a) = 10 (1)
v sin(a)...
so it's shape is a parabola
fiery pelican
OK.
earnest widget
if you are confused then I'll sketch it
fiery pelican
I saw that other things should be involved.
fiery pelican
But Thank you.