A volleyball is served at a speed of 8.0 m/s at an angle 35° above the horizontal.What is the speed of the ball when received by the opponent at the same height?
same as when it was hit, but going down, instead of up.
To find the speed of the ball when it is received by the opponent, we can break down the initial velocity into its horizontal and vertical components.
The horizontal component of the velocity remains constant throughout the ball's flight, as there is no acceleration in that direction. Therefore, the horizontal component of the velocity remains at 8.0 m/s.
The vertical component of the velocity changes due to the influence of gravity. We can calculate the vertical component using the following equation:
Vf = Vi + at
Where:
Vf = final velocity
Vi = initial velocity
a = acceleration (in this case, due to gravity)
t = time
Since we are interested in finding the vertical component of the final velocity when the ball is received by the opponent, we need to determine the time it takes for the ball to reach that point.
To find the time, we can use the equation:
y = Viy * t + (1/2) * a * t^2
Where:
y = vertical displacement (in this case, 0 as the height remains the same)
Viy = initial vertical velocity
a = acceleration (in this case, due to gravity)
t = time
Since the ball is served at an angle of 35° above the horizontal, we can find the initial vertical velocity (Viy) using the equation:
Viy = Vi * sin(θ)
Where:
Vi = initial velocity
θ = angle with respect to the horizontal
Plugging in the values:
Viy = 8.0 m/s * sin(35°) = 4.57 m/s
Now, we can use this value to find the time it takes for the ball to reach the same height when received by the opponent. We rearrange the equation:
y = Viy * t + (1/2) * a * t^2
0 = (4.57 m/s) * t + (1/2) * (-9.8 m/s^2) * t^2
This equation is a quadratic equation, and solving it will give us the time it takes for the ball to reach the opponent. Once we have the time, we can calculate the final velocity using:
Vf = Vi + at
In this case, the final velocity (Vf) will be the magnitude of the resulting velocity, as the ball lands at the same height as it was when it was served.