Question

multiple choice identify the choice that best completes the statement or answers the question. 1. a projectile is launched horizontally and hits the ground in 0.5 second. if it is launched horizontally with twice the speed in the same direction, then it would hit the ground in _. a. the same amount of time b. in twice the time c. in half the time d. in more time than 0.50 second but less time than 1.00 second the figure above shows the path of a ball tossed from a building. air resistance is ignored. 2. at what point of the ball’s path shown in the figure above is the vertical component of the ball’s velocity zero? a. a b. b c. c d. d 3. in the figure above, at which point is the magnitude of the ball’s vertical speed about equal to the speed at which it was tossed? a. a b. b c. c d. d 4. the x & y components of the vector on the left are represented by which choices on the right? 5. a ball tossed from level ground hits the field some distance away. if there is no air resistance, the time that it takes the ball to rise to its peak must be... a. greater than the time it takes to fall back down b. equal to the time it takes to fall c. less than the time it takes to fall

Explanation:

Step1: Analyze projectile - horizontal motion

In projectile motion, horizontal and vertical motions are independent. Changing the horizontal speed does not affect the vertical motion. The time - of - flight of a horizontally launched projectile is determined by the vertical motion and the height from which it is launched. Using the equation for vertical displacement $y = v_{0y}t+\frac{1}{2}gt^{2}$, where $v_{0y} = 0$ (horizontally launched), $y=-h$ (downward displacement), and $h=\frac{1}{2}gt^{2}$. Since the height $h$ is the same, the time $t$ is the same. So for the first question, the answer is a.

Step2: Identify vertical - velocity zero point

At the highest point of a projectile's path, the vertical component of the velocity is zero. In the given ball's path, point B is the highest point. So for the second question, the answer is b.

Step3: Analyze vertical speed symmetry

In the absence of air resistance, the vertical motion of a projectile is symmetric. The speed of the ball when it reaches the same height as the launch point on the way down is the same as the vertical speed at launch. Point D is at the same height as the launch point. So for the third question, the answer is d.

Step4: Determine vector components

For a vector pointing upwards and to the left, the x - component is negative (left - direction) and the y - component is positive (up - direction). So for the fourth question, the answer is C.

Step5: Analyze time - of - flight symmetry

In the absence of air resistance, the time it takes for a ball tossed from level ground to rise to its peak is equal to the time it takes to fall back down. This is because the acceleration due to gravity is constant and the motion is symmetric. So for the fifth question, the answer is b.

Answer:

1. a. the same amount of time
2. b. B
3. d. D
4. C
5. b. Equal to the time it takes to fall