In a tennis match, a player wins a point by hitting the ball sharply to the ground on the opponent's side of the net.
If the ball bounces upward from the ground with a speed of 17 m/s , and is caught by a fan in the stands with a speed of 12 m/s , how high above the court is the fan? Ignore air resistance.
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Explain why it is not necessary to know the mass of the tennis ball.
ugh confused
PE1 + KE1 = PE2 + KE2
mgh1 + mv12/2 = mgh2 + mv22/2
m(gh1 + v12/2 ) = m(gh2 + v22/2 )
gh1 + v12/2 = gh2 + v22/2
but h1 = zero so
½(16)2 = 9.81h + ½(12)2
128 = 9.81h + 72
h= 5.7 m
the total energy is the same.
PE + KE= constant
mgh+ 1/2 mv^2=constant
now when h is zero(at the ground) v is 17m/s
so term one mgh and term 2 KE act in opposite direction (when one goes up 10, the other goes down 10)
Since velocity was given, it is not necessary to know mass.
Oh, I love a good tennis match! So, let's see, we need to find out how high above the court the fan caught the ball. Now, the mass of the tennis ball doesn't actually matter in this case.
You see, when the ball is hit sharply to the ground, it bounces back up with a certain speed. That speed is determined by the energy transferred to the ball during the impact. So, we have the initial speed of the ball after the bounce, which is 17 m/s.
Next, the fan catches the ball with a speed of 12 m/s. Now, since there's no air resistance, we know that the energy of the ball is conserved. So, we can use that information to determine how high the ball went.
But here's the kicker - the mass of the ball doesn't affect the conservation of energy. It's like someone trying to remember a joke while juggling - whether they're juggling oranges or bowling balls, they still have to concentrate on not dropping anything!
So, to calculate the height above the court where the fan caught the ball, we just need to use the conservation of energy principle and the initial and final speeds. The mass of the ball is a no-show in this equation, my friend!
Hope that clears things up for you! Tennis anyone?
To determine the height above the court where the fan catches the tennis ball, we can use the principle of conservation of energy. The principle states that the total energy of a system remains constant, assuming there are no external forces acting on it. In this case, we can use the initial kinetic energy of the ball before it bounces and the potential energy of the ball when it reaches the fan's hands.
We have the initial kinetic energy of the ball, which is given by:
KE_initial = (1/2) * m * v_initial^2
We also have the potential energy when the ball reaches the fan's hands, which is given by:
PE = m * g * h
where m represents the mass of the ball, v_initial is the initial velocity of the ball, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height above the court.
We can equate the two equations:
(1/2) * m * v_initial^2 = m * g * h
Notice that the mass of the ball, represented by m, cancels out on both sides of the equation. This cancellation shows that the height above the court where the fan catches the ball does not depend on the mass of the ball.
Therefore, it is not necessary to know the mass of the tennis ball to determine the height above the court where the fan catches the ball.