To make a bounce pass, a player throws a 0.70-basketball toward the floor. The ball hits the floor with a speed of 5.9 at an angle of 70 to the vertical.If the ball rebounds with the same speed and angle, what was the impulse delivered to it by the floor?
Your numbers need dimensions. That is one of the first things you should have learned about physics.
The impulse delivered by the floor equals the momentum change of the basketball due to the bounce. Momentum changes perpendicular to the floor only.
To calculate the impulse delivered to the basketball by the floor, we can use the principle of conservation of momentum.
The impulse of an object is given by the change in momentum it experiences. In this case, the basketball is thrown towards the floor, and after rebounding, it moves in the opposite direction.
First, let's determine the initial momentum of the basketball before it hits the floor. Momentum is equal to the product of mass and velocity.
Given:
- Mass of the basketball (m) = 0.70 kg
- Velocity before hitting the floor (v) = 5.9 m/s
Momentum before hitting the floor (p₁) = m * v
= 0.70 kg * 5.9 m/s
Next, we need to find the final momentum of the basketball after rebounding. The angle of reflection is the same as the angle of incidence, which in this case is 70° to the vertical. We need to calculate the vertical and horizontal components of velocity after rebounding.
Vertical component of velocity (v₂y) = v * sin(angle)
= 5.9 m/s * sin(70°)
Horizontal component of velocity (v₂x) = v * cos(angle)
= 5.9 m/s * cos(70°)
Since the ball rebounds with the same speed and angle, the vertical component of velocity after rebounding (v₂y) will have the same magnitude but opposite direction.
Therefore, the final momentum of the basketball after rebounding is given by:
Momentum after rebounding (p₂) = m * (-v₂y)
Substituting the values into the equation, we get:
Momentum after rebounding (p₂) = 0.70 kg * (-5.9 m/s * sin(70°))
Finally, to calculate the impulse delivered to the basketball by the floor, we need to find the change in momentum, which is the difference between p₂ and p₁.
Impulse delivered to the ball = p₂ - p₁
You can now plug in the values and compute the impulse using the above formula to determine the answer.