To get to the net, a soccer ball must travel 35 m/s [S 40° W]. If one player kicks it 25 m [E], what displacement must be achieved by the second player’s kick?
We can start by breaking down the initial velocity of the ball into its x and y components:
vx = 35 m/s cos(40° W) = 26.8 m/s [E]
vy = 35 m/s sin(40° W) = 22.5 m/s [S]
Now we know that the first player kicks the ball 25 m [E], so the ball's x-displacement is already taken care of. We just need to find the y-displacement required for the ball to reach the net.
Using the kinematic equation:
yf = yi + vy*t + (1/2)gt^2
where yf is the final height (in this case, 0 since the net is on the ground), yi is the initial height (also 0), t is the time of flight, and g is the acceleration due to gravity (-9.8 m/s^2).
We can solve for t by:
t = (-vy ± √(vy^2 - 4(-1/2)(-9.8)(0))) / (2(-1/2)(-9.8))
t = 4.55 s
Now we can use the x-displacement and the time of flight to find the required y-displacement:
y = vy * t + (1/2)gt^2
y = (22.5 m/s) (4.55 s) + (1/2)(-9.8 m/s^2)(4.55 s)^2
y = 52 m [S]
Therefore, the second player's kick must achieve a y-displacement of 52 m [N] in order to get the ball to the net.