A tennis ball of mass= 0.058 kg and speed= 19 m/s strikes a wall at a 45 degree angle and rebounds with the same speed at 45 degrees.
What is the magnitude of the impulse given to the ball?
Only the momentum component perpendicular to the wall changed.
The change,
2M*V cos 45,
equals the impulse given
Velocity of boat relative to the river(vbr):3 km/hr, velocity of river relative to ground(vrg) :2 km/hr. Velocity of boat relative to the ground(vbg): square root of 9+4
To find the magnitude of the impulse given to the ball, we can use the impulse-momentum theorem:
Impulse = Change in Momentum
Momentum is given by the product of mass and velocity:
Momentum = mass * velocity
The initial momentum of the ball before it strikes the wall can be found using the given mass and speed:
Initial Momentum = mass * initial velocity
The final momentum of the ball after it rebounds can also be found using the given mass and speed:
Final Momentum = mass * final velocity
Since the ball rebounds with the same speed, the magnitude of the final velocity is the same as the magnitude of the initial velocity.
Now, let's calculate the initial and final momenta:
Initial Momentum = 0.058 kg * 19 m/s = 1.102 kg∙m/s (rounding to three decimal places)
Final Momentum = 0.058 kg * 19 m/s = 1.102 kg∙m/s (rounding to three decimal places)
The momentum does not change, which means the change in momentum is zero. Therefore, the magnitude of the impulse given to the ball is also zero.
Magnitude of Impulse = 0 (no units)
To find the magnitude of the impulse given to the ball, we can use the equation:
Impulse = Change in momentum
First, let's find the momentum of the ball before and after the collision.
The momentum before the collision, denoted as p1, can be calculated using the equation:
p1 = mass * velocity
p1 = 0.058 kg * 19 m/s
Next, we need to find the momentum after the collision. Since the ball rebounds with the same speed, the magnitude of the velocity remains constant. However, the direction of the momentum changes. To account for the change in direction, we need to calculate the x and y components of the momentum after the collision.
The x and y components of the momentum can be found using the equations:
px = magnitude of momentum * cos(angle)
py = magnitude of momentum * sin(angle)
Since the angle is given as 45 degrees and the magnitude of the momentum remains constant, we have:
px = p1 * cos(45 degrees)
py = p1 * sin(45 degrees)
Now, we can find the momentum after the collision:
p2 = ((px)^2 + (py)^2)^(1/2)
Finally, we can calculate the change in momentum:
Change in momentum = p2 - p1
The magnitude of the impulse given to the ball is equal to the absolute value of the change in momentum.
Therefore, the magnitude of the impulse given to the ball can be determined by plugging in the values:
Impulse = |p2 - p1|