The concept required to solve this problem is conservation of energy.
Initially, calculate the kinetic and potential energy of the balls. Finally, rank the baseballs based on their respective final velocities.
The law of conservation of energy states that the gain in the kinetic energy is equal to the loss in the potential energy.
The expression is as follows:
Here, is the initial and final potential energy respectively and is the initial and final kinetic energy respectively.
The expression foe the kinetic energy is as follows:
Here, m is the mass of the object and v is the velocity of an object.
The expression for the potential energy is as follows:
Here, g is the acceleration due to gravity and h is the height.
The longer the ball is in the air, the longer it will take to hit the ground. And, larger the final velocity will be when the ball hits the ground.
The balls are thrown from the same height. Thus, the potential energy will be the same for all the balls. Also, when the ball reaches the ground the change in potential energy would also be the same.
According, to the conservation of energy the loss in potential energy is equal to the gain in kinetic energy. Hence the change in potential energy for the balls would be equal to the change in kinetic energy. Also, since the change in potential energy is the same for all the balls the change in kinetic energy will also be the same.
Further since the initial speed of all the balls are same, the final speed will also be the same.
Hence the speed of all the baseballs as they hit the ground would be the same.
Let all the baseballs be thrown from a height with an initial velocity .
For case1,
The loss in potential energy is,
The gain in kinetic energy is,
Apply the law of conservation of energy.
Substitute for and
Here, is the final velocity and is the mass of the baseball.
Similarly, for case2,
The final velocity of baseball 2 will be,
The final velocity of baseball 3 will be,
The final velocity of baseball 4 will be,
The final velocity of baseball 5 will be,
The final velocity of baseball 6 will be,
From the expression for it is clear that .
Ans:The ranking of the six baseballs is .
Six baseball throws are shown below. In each case the baseball is thrown at the same initial speed and from the same...
Projectile Motion Ranking TaskSix baseball throws are shown below. In each case, the ball is thrown with speed v at an angle θ from the horizontal. In all cases, the baseball is thrown from the same height H above the ground. Assume for the basis of these rankings that the effects of air resistance are negligible.Part ARank these throws based on the maximum height reached by the ball.Rank from largest to smallest. To rank items as equivalent, overlap them.Part BThis...
Three identical balls are thrown from the top of a building, all with the same initial speed. The first is thrown horizontally, the second at some angle above the horizontal, and the third at some angle below the horizontal. Neglecting air resistance, rank the speeds of the balls at the instant each hits the ground.
Six baseball throws are shown below. In each case, the ball is thrown with speed at an angle from the horizontal. In all cases, the baseball is thrown from the sameheight above the ground. Assume for the basis of these rankings that the effects of air resistance are negligible.Rank these throws based on the maximum height reached by the ball.Rank from largest to smallest.a. v=15 m/s Theta=60 degreesb.v=15m/s Theta=45 degreesc. v=10m/s theta =90 degreesd. v=10m/s theta=60 degreese.v=15 m/s theta =30...
projectile motion Rank these throws based on the maximum height reached by the ball. Rank from largest to smallest. To rank items as equivalent. overlap them. Rank these throws based on the maximum height reached by the ball. Rank from largest to smallest. To rank items as equivalent. overlap them.
Conservation of Energy Ranking Task Six pendulums of various masses m are released from various heights h above a tabletop, as shown in the figures below. All the pendulums have the same length and are mounted such that at the vertical position their lowest points are the height of the tabletop and just do not strike the tabletop when released. Assume that the size of each bob is negligible. Rank each pendulum on the basis of its initial gravitational potential...
Rank from largest to smallest. To rank items as equivalent, overlap them I rope is pulled to the right at a 1 of 2> MacBook Air speed. Rank from largest to smallest. To rank items as equivalent, overlap them. rope is pulled to the right at a C) 2012 MacBook Air Rank from largest to smallest. To rank items as equivalent, overlap them I rope is pulled to the right at a 1 of 2> MacBook Air speed. Rank from...
Rank these throws based on the maximum height reached by the ball. Rank from largest to smallest. To rank items as equivalent, overlap them.
Six artificial satellites circle a space station at constant speed. The mass m of each satellite, distance L from the space station, and the speed v of each satellite are listed below. The satellites fire rockets that provide the force needed to maintain a circular orbit around the space station. The gravitational force is negligible. A.)Rank each satellite based on its period. Rank from largest to smallest. To rank items as equivalent, overlap them. B.)Rank each satellite based on its...
A baseball is thrown from the roof of 20.6 m -tall building with an initial velocity of magnitude 12.4 m/s and directed at an angle of 55.6 ∘ above the horizontal. a) What is the speed of the ball just before it strikes the ground? Use energy methods and ignore air resistance. b) What is the answer for part (A) if the initial velocity is at an angle of 55.6 ∘ below the horizontal? c) If the effects of air...
A ball is thrown with an initial speed of 20 m/s at an angle of 60° to the ground. If air resistance is negligable, what is the ball’s speed at the instant it reaches its maximum height from the ground?