A ball is thrown horizontally off a building that is 30 m high with an initial velocity of 3 m/s.if an identical ball is thrown again horizontally from the same height with 6 m/s, what happens to the flight time?
A. Flight time is doubled.
B. Flight time is decreased by half.
C. Flight time is the same.
D. Flight time is exponentially increased.
I don't understand the material very well. If you could explain and tell me, I'd appreciate it. Thanks in advance!
flight time is determined by the falling height: the building did not change height.
To answer the question, we need to understand the relationship between the initial horizontal velocity of a projectile and the time of flight.
When a ball is thrown horizontally, it has an initial vertical velocity of zero. The only force acting on the ball vertically is gravity, which causes it to accelerate downward at a constant rate. However, there is no force acting on the ball horizontally, so it maintains a constant horizontal velocity throughout its flight.
Since the ball is thrown horizontally, the vertical motion can be treated independently. The time of flight for a projectile is determined solely by the vertical motion, specifically by the time it takes for the ball to reach the ground.
Using the equations of motion, we can calculate the time of flight for each ball. The equation we use is:
t = √(2h/g)
where t is the time of flight, h is the initial vertical height, and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Let's calculate the time of flight for the first ball:
t1 = √(2 * 30 / 9.8)
≈ √6.122
≈ 2.47 s (rounded to two decimal places)
Now, let's calculate the time of flight for the second ball:
t2 = √(2 * 30 / 9.8)
≈ √3.061
≈ 1.75 s (rounded to two decimal places)
Comparing t1 and t2, we can see that the flight time for the second ball (thrown with a velocity of 6 m/s) is smaller than the flight time of the first ball (thrown with a velocity of 3 m/s).
Therefore, the answer to the question is B. Flight time is decreased by half.
To find out what happens to the flight time when the initial velocity is doubled, we need to understand the factors that affect the flight time of a horizontally thrown ball.
When a ball is thrown horizontally, there is no initial vertical velocity. This means that the only force acting on the ball is gravity, pulling it down. As a result, the ball follows a parabolic trajectory called a projectile motion.
The time it takes for the ball to reach the ground is called the flight time. The flight time depends on the vertical distance the ball travels, which is determined by the initial height of the building.
In this case, both balls are thrown horizontally from the same height of 30 m. Since their initial heights are the same, we can conclude that the vertical distance they travel is also the same. Therefore, the flight time will be the same for both balls.
So, the correct answer is C. Flight time is the same.
To further clarify, the horizontal component of the initial velocity does not affect the flight time, as the ball does not experience any horizontal acceleration or forces.
Remember that this explanation assumes there are no other factors such as air resistance or variations in the gravitational field that could affect the flight time. In a controlled environment, the flight time would remain the same.