Two objects are launched with the same initial horizontal velocity, but one has twice the initial vertical velocity as the other. Which of the following statements is true?
One has twice the total speed as the other
They have the same acceleration
They have the same max height
One travels twice as far as the other.
C
The horizontal speed does not affect the vertical speed, so both rise to the same height.
Just as when you drop one rock and throw the other horizontally. They both hit the ground at the same time.
To determine which statement is true, let's analyze the motion of the two objects.
Both objects are launched with the same initial horizontal velocity, which means their horizontal velocities remain constant throughout their motion. Therefore, we can ignore the horizontal component and focus on the vertical component.
The initial vertical velocity of one object is twice that of the other. Let's denote the initial vertical velocity of the first object as V1 and the initial vertical velocity of the second object as V2. Since V1 = 2V2, we can conclude that the first object has twice the initial vertical velocity as the second object.
Now let's evaluate each of the statements:
1. One has twice the total speed as the other: This statement is false. The total speed of an object is the magnitude of its velocity vector, which is given by the square root of the sum of the squares of its horizontal and vertical velocities. Since the horizontal velocities are the same for both objects and only the vertical velocities differ, the total speeds will not be twice as much for one object compared to the other.
2. They have the same acceleration: This statement is true. The acceleration due to gravity, which acts vertically downward, is the same for both objects. In the absence of other external forces, the only force acting on the objects is gravity, and it provides the same acceleration to both.
3. They have the same max height: This statement is false. The maximum height reached by an object in projectile motion depends on its initial vertical velocity. Since the first object has twice the initial vertical velocity, it will reach a higher maximum height compared to the second object.
4. One travels twice as far as the other: This statement is true. The horizontal distance traveled by an object in projectile motion is determined by its horizontal velocity and the time of flight. Since both objects have the same horizontal velocities and the time of flight only depends on the vertical motion, the time of flight will be the same for both objects. Therefore, the first object, with a higher initial vertical velocity, will spend more time in the air and thus travel a greater horizontal distance compared to the second object.
So, the correct statement is: One travels twice as far as the other.