Two balls having different masses reach the same height when shot into the air from the ground.
If there is no air drag, which of the following statements must be true? (More than one statement may be true.)
A. Both balls left the ground with the same speed.
B. Both balls left the ground with the same kinetic energy.
C. Both balls will have the same gravitational potential energy at the highest point.
D. The heavier ball must have left the ground with a greater speed than the lighter ball.
E. Both balls have no acceleration at their highest point.
A. is true if the balls were thrown at the same angle. That should have been specified.
None of the other ststements are true.
The acceleration is always -g for both, while in the air.
Well, let me clown around with this question for a second!
A. Both balls left the ground with the same speed. - Hmm, not necessarily. They could have left with different speeds, it's just that they reached the same height.
B. Both balls left the ground with the same kinetic energy. - No, no! The kinetic energy depends on the mass and the velocity, so if the masses are different, the kinetic energy could be different too.
C. Both balls will have the same gravitational potential energy at the highest point. - Yup, that's true! The height is the same, so their potential energy will be the same.
D. The heavier ball must have left the ground with a greater speed than the lighter ball. - Nope, that's not true. The masses don't determine the speed at which the balls left the ground, just their ability to resist changes in motion.
E. Both balls have no acceleration at their highest point. - Absolutely correct! At the highest point, their velocity is zero, and if there's no acceleration, then there's no net force acting on them.
So, the correct answers are C and E. Keep clowning with physics!
Statement A: Both balls left the ground with the same speed.
This statement is false. The speed at which an object is launched into the air depends on the initial velocity given to it. In this case, the masses of the balls are different, and hence, their initial velocities could be different as well.
Statement B: Both balls left the ground with the same kinetic energy.
This statement is false. Kinetic energy depends on both mass and velocity. Since the masses of the balls are different, their kinetic energy could be different as well, even if they reach the same height.
Statement C: Both balls will have the same gravitational potential energy at the highest point.
This statement is true. Gravitational potential energy depends on the height of the object and the acceleration due to gravity, but not on the mass. Since both balls reach the same height, their gravitational potential energy at the highest point will be the same.
Statement D: The heavier ball must have left the ground with a greater speed than the lighter ball.
This statement is false. In the absence of air drag, the mass of an object does not affect its launch speed. Both balls could have left the ground with different speeds, depending on the initial velocity given to them.
Statement E: Both balls have no acceleration at their highest point.
This statement is true. At the highest point of their trajectory, both balls have zero vertical velocity. Since acceleration is defined as the rate of change of velocity, and the velocity is zero, the acceleration in the vertical direction at the highest point is also zero.
To determine which statements are true, we need to understand the principles of energy conservation and projectile motion.
When a ball is shot into the air, it undergoes projectile motion and experiences only the force of gravity acting on it. The key concept here is that energy is conserved, meaning the total energy of the system remains constant.
Let's evaluate each statement:
A. Both balls left the ground with the same speed.
For this statement to be true, the balls must reach the same height. According to the principle of conservation of energy, the initial kinetic energy of the ball will be converted entirely into gravitational potential energy at the highest point. Therefore, if both balls reach the same height, they must have left the ground with the same speed. This statement is true.
B. Both balls left the ground with the same kinetic energy.
Kinetic energy is given by the formula KE = (1/2)mv^2, where m is the mass and v is the velocity of the object. Since the balls have different masses, their kinetic energies will be different if their velocities are not the same. Therefore, this statement is not necessarily true.
C. Both balls will have the same gravitational potential energy at the highest point.
At the highest point, the balls will have converted their entire initial kinetic energy into gravitational potential energy. The amount of gravitational potential energy is given by PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height. If both balls reach the same height, and since they have different masses, they will have different amounts of gravitational potential energy. Therefore, this statement is not true.
D. The heavier ball must have left the ground with a greater speed than the lighter ball.
This statement is not necessarily true. The mass of the ball does not directly impact its speed. As long as both balls reach the same height, their initial speeds can be different, depending on their masses.
E. Both balls have no acceleration at their highest point.
At the highest point, the balls will momentarily stop and change direction. This means that their velocity is zero at the highest point. Since acceleration is the rate of change of velocity, the balls will have zero acceleration at their highest point. Therefore, this statement is true.
In conclusion:
Statement A is true.
Statement B is not necessarily true.
Statement C is not true.
Statement D is not necessarily true.
Statement E is true.