The collision with the building causes the car to come to a stop in approximately 1 second. The impulse-momentum equation which is the same thing as Newton’s second law stated in terms of momentum isĪ car traveling at 27 m/s collides with a building. This problem involves only one dimension because the ball starts from having no horizontal velocity component before impact. But since the force of the racquet is significantly larger than the gravitational force, we can ignore the gravitational force. From this, we can obtain the acceleration.Īt the instant the ball is hit, the forces acting on the ball are the gravitational force applied by Earth and the force of the racquet. The horizontal velocity of the ball changes from 0 to 58m/s in 5.0ms. Using impulse-momentum equation, which is Newton’s Second Law in the form of.Using kinematics equations along with Newton’s Second law in the form of.There are two ways to solve this problem: What is the average force exerted on the 0.057-kg tennis ball by Venus Williams’ racquet, assuming that the initial horizontal component of the ball’s velocity before impact is negligible and that the ball remained in contact with the racquet for 5.0 ms (milliseconds)? So that's an impulse of 2.4 kilograms meters per second away from the wall.During the 2007 French Open, Venus Williams hit the fastest recorded serve in a premier women’s match, reaching a speed of 58 m/s (130 mph). So x-component initial of the velocity is the velocity multiplied by sin 45 in this triangle here, the x-component is the opposite leg and we have negative 2 times 0.06 kilograms- mass of the ball-times its initial speed of 28 meters per second times sin 45 that gives negative 2.4 kilograms meters per second. And well these two terms are the same so we collect them and that makes negative 2 m v x i. I guess, you know, more precisely I could have written v x f equals negative v x i but it's the same idea so this is the substitution I just made here. And so we have m x-component velocity final minus m x-component velocity initial and then we substitute in negative v x i in place of v x f based on this. Normally, impulse would be the vector sum of the impulses in each component in each direction so we would normally have to do Pythagoras to get the impulse but in this case, there is no impulse in the y-direction so this is just the square root of ΔP x squared which is just ΔP x as I have written here. So impulse then is gonna be just to do with the x-direction, there is no change in momentum in the y-direction so that's why we can say this. So the initial y-component of the velocity is the same as the final y-component of the velocity as I was saying and the initial x-component of its velocity is the negative of the x-component of its velocity after colliding with the wall same magnitude, opposite direction. So we'll take positive to be to the right and upwards as well. However, the x-component of its velocity has the same magnitude in both cases but technically, the velocity does change because its direction changes and so it has a different sign. So in both cases, given that it has the same speed we are told, the vertical component of its velocity will be the same in both cases and so that means it doesn't change at all. Before and after colliding with a wall, this ball has the same angle with respect to the vertical- it's still 45 degrees here with respect to vertical initially- and then its velocity is 45 degrees with respect to vertical after colliding with a wall.
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