**Physics Problem: Projectile Motion****Problem Statement:**Alice shoots a pebble horizontally with her slingshot from a window that is at a height \(H\) and it lands a distance \(D\) away from the building. She then shoots a pebble with the same initial velocity from a different window, but this time the pebble lands a distance \(D/2\) away. How high is the window from which Alice takes the second shot?- A. \(4H\)- B. \(2H\)- C. \(H\)- D. \(H/2\)- E. \(H/4\) (Highlighted as the correct answer)**Solution Explanation:**To solve this problem, we need to understand the concepts of projectile motion and the relationship between the horizontal distance (range) and the height from which the object is projected.### Step-by-Step Solution:1. **Understanding Initial Conditions:** - The first shot: - Height: \( H \) - Horizontal distance: \( D \)2. **Second Shot:** - Height: Unknown (let's denote it as \( h \)) - Horizontal distance: \( D / 2 \)3. **Important Equations:** - The horizontal distance (range) for a projectile shot with an initial horizontal velocity \( v \) and time of flight \( t \) is given by: \[ R = vt \] - The time of flight \( t \) of the projectile depends on the height \( h \) from which it is shot: \[ t = \sqrt{\frac{2h}{g}} \] Where \( g \) is the acceleration due to gravity.4. **For the First Shot:** - The time of flight from height \( H \): \[ t_1 = \sqrt{\frac{2H}{g}} \] - The horizontal range: \[ D = v t_1 = v \sqrt{\frac{2H}{g}} \]5. **For the Second Shot:** - The time of flight from height \( h \): \[ t_2 = \sqrt{\frac{2h}{g}} \] - The horizontal range: \[ \frac{D}{2} = v t_2 = v \sqrt{\frac{2h}{g

Answered: Image /qna-images/answer/bd898558-8344-48f1-921f-8bff580dd003.jpg

Alice shoots a pebble horizontally with her slingshot from a window that is at a height H and it lands a distance D away from the building. She then shoots a pebble with the same initial velocity from a different window, but this time the pebble lands a distance D/2 away. How high is the window from which Alice takes the second shot? A. 4H B. 2H C. H D. H/2 E. H/4

Alice shoots a pebble horizontally with her slingshot from a window that is at a height H and it lands a distance D away from the building. She then shoots a pebble with the same initial velocity from a different window, but this time the pebble lands a distance D/2 away. How high is the window from which Alice takes the second shot? A. 4H B. 2H C. H D. H/2 E. H/4

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Related questions

Q: . Challenge Problem: Pepper Potts is dropped from a helicopter! Iron Man is standing on top of a…

Q: A ball is thrown horizontally from the top of a building 22m high.the ball strikes the ground at a…

Q: Juan throws a baseball with an initial speed of 40 m/s at an angle of 53 0 above the horizontal.…

A: Given data The initial speed of the baseball is: u = 40 m/s The baseball is thrown at an angle of θ…

Q: 6) A projectile is fired at an inclination of 45° to the horizontal, with a muzzle velocity of 100…

A: Given The angle of inclination is θ = 45o. The muzzle velocity is u = 100 ft/s. The height of the…

Q: Your little sister is running to the park in your neighborhood at a speed of 3.90 m/s when you…

A: Given, Speed of running v1 = 3.90 m/s Height h = 45 m Time t1 = 8 sec So the time the ball take is…

Q: An archer aims directly at an apple attached to a tree branch a horizontal distance d away and a…

A: let the initial veocity is v.

Q: A projectile is fired upward with an initial velocity of 80 m/s and it falls a horizontal distance…

Q: Which of the following will reach the maximum height? a. A golf ball is hit at an angle of 45°…

A: A) Given Data : The angle of the launch of the golf ball is given as θA=450 The initial speed of the…

Q: You are walking around your neighborhood and you see a child on top of a roof of a building kick a…

A: The vertical component of the initial velocity of the object is, vy,o=v0sinθ=10 m/ssin50°=7.66 m/s…

Q: 35.0° above the ground. a. How much time does it take for the ball to reach the goal posts? b. How…

A: Let the velocity of the ball is u. Let the angle with which the goal kicker kicks the ball is θ. Let…

Q: 6. In lab you shot a projectile off of the edge of a table at an angle of 30° with a speed of 2.5…

A: Initial velocity of projectile, u = 2.5 m/sec Angle of motion = 30 degree Range of projectile, R =…

Q: A pitcher throws an overhand fastball from an approximate height of 2.65 m and at an angle of 2.5…

A: Given:Inital height, yi = 2.65 mAngle of throw, θ = 2.5o below horizontal (as shown in figure…

Q: 8. A football quarterback throws a pass to a receiver at an angle of 25 degrees to the horizontal…

A: Given, Initial velocity,v=25 m/s Angle of launch, θ=25° Initial distance of receiver, x=30 m

Q: A projectile is thrown up from the ground with velocityV = 60î + 80j at 53° above the horizontal.…

Q: A cannon at an elevation of 2000 feet above sea level fires a missile upward at an angle of 45…

A: We will answer the question using kinematic equations of motion. The detailed steps are as follows.

Q: A boy is standing from the top of a cliff 8 m from the ground and he has a bow which is aimed 40…

Q: A ball rolls off a horizontal roof. The edge of the roof is 14.0 m above the ground, and the ball…

Q: When the dried-up seed pod of a scotch broom plant bursts open, it shoots out the seed with an…

A: A) Apply the second kinematic equation along the vertical direction and substitute the required…

Q: 5. A projectile is fired at a 60° angle as shown below. The projectile reaches a maximum height ymas…

Q: A.With what vertical speed does the ball leave the ground (V yi)? Possible answers: +30 -30 +21…

Q: A pendulum of length L = 0.98 m hangs at rest with 2.0 kg bob. The string is of negligible mass. A…

A: As this is multiple question, according to policy we will answer first question. Let first find out…

Q: 3. A student standing on a 25 m building wishes to hit a target which is 7 m tall and 40 m away. The…

Q: *41. Go mmh A soccer player kicks the ball toward a goal that is 16.8 m in front of him. The ball…

Question

**Physics Problem: Projectile Motion**

**Problem Statement:**

Alice shoots a pebble horizontally with her slingshot from a window that is at a height \(H\) and it lands a distance \(D\) away from the building. She then shoots a pebble with the same initial velocity from a different window, but this time the pebble lands a distance \(D/2\) away. How high is the window from which Alice takes the second shot?

- A. \(4H\)
- B. \(2H\)
- C. \(H\)
- D. \(H/2\)
- E. \(H/4\) (Highlighted as the correct answer)

**Solution Explanation:**

To solve this problem, we need to understand the concepts of projectile motion and the relationship between the horizontal distance (range) and the height from which the object is projected.

### Step-by-Step Solution:

1. **Understanding Initial Conditions:**
- The first shot:
- Height: \( H \)
- Horizontal distance: \( D \)

2. **Second Shot:**
- Height: Unknown (let's denote it as \( h \))
- Horizontal distance: \( D / 2 \)

3. **Important Equations:**
- The horizontal distance (range) for a projectile shot with an initial horizontal velocity \( v \) and time of flight \( t \) is given by:
\[ R = vt \]
- The time of flight \( t \) of the projectile depends on the height \( h \) from which it is shot:
\[ t = \sqrt{\frac{2h}{g}} \]
Where \( g \) is the acceleration due to gravity.

4. **For the First Shot:**
- The time of flight from height \( H \):
\[ t_1 = \sqrt{\frac{2H}{g}} \]
- The horizontal range:
\[ D = v t_1 = v \sqrt{\frac{2H}{g}} \]

5. **For the Second Shot:**
- The time of flight from height \( h \):
\[ t_2 = \sqrt{\frac{2h}{g}} \]
- The horizontal range:
\[ \frac{D}{2} = v t_2 = v \sqrt{\frac{2h}{g

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Basics :

VIEW

Step 2: Concepts :

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

You are walking around your neighborhood and you see a child on top of a roof of a building kick a soccer ball. The soccer ball is kicked at 33° from the edge of the building with an initial velocity of 19 m/s and lands 55 meters away from the wall. How tall, in meters, is the building that the child is standing on? y m 20
1. A projectile is shot upward at a 60.° angle with the ground at 65 m/s. a) What is the velocity of the projectile after 1.7s? b) How far away from the launch point will the projectile land?
A cannon ball is fired at a wall that is 300 m away on level ground. The initial velocity of the cannon is 89 m/s, 40° above the horizontal. Don't assume the ball hits the wall at maximum height! What is the y-component of the ball's velocity when the ball hits the wall? h V; = 89 m/s 40° 300 m O 89.0 m/s O 9.81 m/s O 7.60 m/s O 18.2 m/s O 14.1 m/s O 2.99 m/s
Two vectors appear as in Figure Q3.21. Which combination points directly to the left? А. Р+0 B. P - Q C. Q – P D. -ğ-P FIGURE Q3.21
A 2.00-m-tall basketball player is standing on the floor 10.0 m from the basket, as in the figure below. If he shoots the ball at a 40.0° angle with the horizontal, at what initial speed must he throw the basketball so that it goes through the hoop without striking the backboard? The height of the basket is 3.05 m. m/s 40.0 2,00 3.05 m 10.0 m
A rescue plane flies at 198km/hr and at a constant elevation of 500m toward a point directly over an accident victim struggling in the sea. The pilot must release a rescue capsule so that it hits the water very close to the victim.a). what should be the angle of the pilot’s line of sight when the capsule is released? EVb) what is the velocity of the rescue in the vertical plane when the capsule is released? APc). as the capsule reaches the water, what is its velocity ?̅in i. the unit vector notation? ANii. magnitude- angle notation
Your nephew got a Nerf Bazooka gun for Christmas, so you take it outside to play with it (just like my uncles did when I was little). The bazooka is on your shoulder, 1.5 m above the ground. You aim the gun 25° above the horizontal and the big, foam projectile leaves the gun with an initial velocity of 36 m You accidentally aim the bazooka at a tree that is a horizontal distance of 27 m away. How long does it take for the projectile to hit the tree? t = How high (above the ground) in the tree does the projectile get stuck? hfinal = m Imagine you were more clever and aimed into an empty field with no obstructions. You can control how fast the projectile leaves the gun by pumping more times or fewer times (more pumps = faster projectile). What are TWO ways you could increase the amount of time that the projectile is in the air?
Your little sister is running to the park in your neighborhood at a speed of 3.90 m/s when you suddenly realize she left her favorite playground ball behind. You throw her ball horizontally out the window of your apartment which is at a height of 45.0 m above the street and directly above the sidewalk. You throw the ball 8.00 seconds after she has passed below your window and she catches the ball! a) Ignoring air resistance, what is the initial speed that you must throw her ball so she can catch it just before it reaches the ground? b) How far down the sidewalk from the window is your sister when she catches her ball?
A car is moving with velocity v as shown. The driver notices a deer ahead then he hits the brake to slow down the car. Which arrow best represents the acceleration vector of the car? O (H) (G) O (F) O (E) ○ (D) (B) ○ (C) O (A) ○ (1) V G. H. B. C. La=0 F D. E.
The archerfish hunts by dislodging an unsuspecting insect from its resting place with a stream of water expelled from the fish's mouth. Suppose the archerfish squirts water with a speed of 2.45 at an angle of 48.0 above the horizontal, and aims for a beetle on a leaf 2.50 above the water's surface. a.) At what horizontal distance from the beetle should the archerfish fire if it is to hit its target in the least time? b.) How much time will the beetle have to react? step by step please!!
5. A projectile is launched at an angle of 50° with the horizontal and a speed of 25 m/s. a) What is the Range of the projectile? b) What is its height after 1.5 second?
A projectile is projected from the origin with a velocity of 30.0 m/s at an angle of 40.0 degrees above the horizontal. What is the time it takes the projectile to reach maximum height? Multiple Choice 2.23 s 1.02 s 1.97 s 1.54 s 2.66 s