A volleyball court is 18 m long from baseline to baseline and the net is 2.24 m high. A volleyball player serves the ball from the baseline by hitting it at a height of 2 m above the floor at an angle of 10 degrees above the horizontal.
A.) If the ball is in the air for 1.05 s, is the serve in or out (assuming it clears the net)?
B.) Does the serve actually clear the net?
It goes up, then down for 1.05 s
do the vertical problem
Hi = 2
final h = 0
h = Hi + Vi t - 4.9 t^2
0 = 2 + 1.05 Vi - 4.9 (1.05)^2
-2 + 5.4 = 1.05 Vi
Vi = 3.24 m/s initial speed up
Now the horizontal problem
max speed * sin 10 = 3.24
so speed = 18.7 m/s
so
u = 18.7 cos 10 = 18.4 m/s
distance = u t = 19.3 meters
so out
time at 9 meters
t = 9/18.4 = .489 seconds to net
h = 2 + 3.24(.489) - 4.9(.489)^2
= 2.41 so it clears the net
Thank you so much!!!!!! :)
To determine if the serve is in or out, we need to find the horizontal distance the ball travels and compare it to the length of the volleyball court.
To find the horizontal distance, we can use the formula:
horizontal distance = initial horizontal velocity * time
In this case, the initial horizontal velocity is the horizontal component of the serve's velocity. Given that the ball is hit at an angle of 10 degrees above the horizontal, we can use trigonometry to find this component:
horizontal velocity = initial velocity * cos(angle)
We are not given the initial velocity directly, but we are given that the ball is hit at a height of 2 m above the floor. Assuming the ball is hit with zero initial vertical velocity (ignoring air resistance), we can use the equation for the vertical motion of an object:
vertical displacement = initial vertical velocity * time + (1/2) * acceleration * time^2
Since the ball starts and ends at a height of 2 m, the vertical displacement is 0. So, we can rearrange the equation to solve for the initial vertical velocity:
initial vertical velocity = -0.5 * acceleration * time
Using the value of acceleration due to gravity (approximately 9.8 m/s^2) and a time of 1.05 s, we can find the initial vertical velocity.
Now that we have the initial velocity and the angle above the horizontal, we can calculate the horizontal component of the velocity and use it to find the horizontal distance.
Once we have the horizontal distance, we can compare it to the length of the volleyball court (18 m) to determine if the serve is in or out.
To check if the ball clears the net, we need to compare the vertical distance reached by the ball to the height of the net (2.24 m). We can use the vertical motion equation again to find the vertical distance:
vertical displacement = initial vertical velocity * time + (1/2) * acceleration * time^2
If the vertical displacement is greater than the height of the net, then the serve clears the net. Otherwise, it does not.