To determine the speed of the volleyball when received by the opponent, we need to consider the horizontal and vertical components of its initial velocity.
Given: Initial speed (serve speed) = 10 m/s Launch angle (above horizontal) = 40 degrees
To find the horizontal component of the initial velocity, we use the equation:
Horizontal velocity = Initial velocity * cos(angle)
Horizontal velocity = 10 m/s * cos(40 degrees)
To find the vertical component of the initial velocity, we use the equation:
Vertical velocity = Initial velocity * sin(angle)
Vertical velocity = 10 m/s * sin(40 degrees)
Since the ball is received at the same height, the vertical velocity at that point would be zero (assuming no air resistance). Therefore, the speed of the ball when received by the opponent will be equal to the horizontal component of its initial velocity.
Speed of the ball when received = Horizontal velocity
Substituting the values:
Speed of the ball when received = 10 m/s * cos(40 degrees)
Calculating the value:
Speed of the ball when received ≈ 7.66 m/s
Therefore, the speed of the ball when received by the opponent at the same height would be approximately 7.66 m/s.