**Projectile Motion Problem****Problem Statement:**A ball is thrown at an angle of 30° from the top of a building 0.10 km high. The ball strikes the ground at a point 125 m horizontally away from and below the point of release. **Questions:**(a) What is the initial speed of the ball?(b) What is the speed of the ball just before it strikes the ground?**Instructions for Solving:**1. **Understand the given information:** - Angle of projection, \( \theta = 30^{\circ} \) - Height of the building, \( h = 0.10 \, \text{km} = 100 \, \text{m} \) - Horizontal distance from the point of release to the point where the ball hits the ground, \( R = 125 \, \text{m} \)2. **Break down the components of the projectile motion:** - Decompose the initial velocity \( v_0 \) into horizontal (\( v_{0x} \)) and vertical (\( v_{0y} \)) components: - \( v_{0x} = v_0 \cos 30^{\circ} \) - \( v_{0y} = v_0 \sin 30^{\circ} \) 3. **Use the kinematic equations to solve for the initial speed \( v_0 \):** - Horizontal motion: \[ R = v_{0x} t \] \[ 125 = v_0 \cos 30^{\circ} \times t \] - Vertical motion: - Use the equation for displacement: \[ y = v_{0y} t - \frac{1}{2} g t^2 \] \[ -100 = (v_0 \sin 30^{\circ})t - \frac{1}{2} g t^2 \]4. **Solve the system of equations to find \( t \) (time of flight) and \( v_0 \):**5. **Calculate the final speed of the ball just before it strikes the ground:** - Use the equations for horizontal and vertical components of velocity just before impact: - \( v_{x} = v_{0x} \) - \( v_{y} = v

Name: **Projectile Motion Problem****Problem Statement:**A ball is thrown a
Uploaded: 2024-03-20T06:57:47.000Z
Channel: Bartleby
Description: **Projectile Motion Problem****Problem Statement:**A ball is thrown at an angle of 30° from the top of a building 0.10 km high. The ball strikes the ground at a point 125 m horizontally away from and below the point of release. **Questions:**(a) Wha

Science

Physics

A ball is thrown at an angle of 30° from the top of a building 0.10 km high. The ball strikes the ground at a point 125 m horizontally away from and below the point of release. (a)What is the initial speed of the ball? (b) What is the speed of the ball just before it strikes the ground?

A ball is thrown at an angle of 30° from the top of a building 0.10 km high. The ball strikes the ground at a point 125 m horizontally away from and below the point of release. (a)What is the initial speed of the ball? (b) What is the speed of the ball just before it strikes the ground?

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: What is the maximum height reached by the object? b) If the object has a time of flight of 2.9 s,…

Q: he edge of the table. (a) How long is the ball in the air? (b) What is its speed at the instant it…

Q: The egg is launched at a speed of 56 m/s at an angle of 73 degrees above the horizontal. At what…

A: Given : Initial velocity of egg, u = 56 m/s Angle made by the path of egg with…

Q: The elevations of the ski jumping hill shown below are as follows: hA = 46 m hB = 2.4 m hC =…

Q: A very bored 318 kg bear decides to jump across a stream. The stream is 6 m wide and the east bank…

A: First, we need to identify the variables from the problem. The bear's initial velocity (vi) is given…

Q: An object is shot straight up from the ground with an initial velocity of 20 m/s. How high above the…

A: Given: The initial speed of the object is 20 m/s. The time interval from maximum height is 1 s.

Q: You toss a pebble from a cliff which is 20 m above the sea below with an initial speed of 15 m/s at…

Q: A stone is thrown horizontally with a speed of 12 m/s from the edge of a 10 m high cliff. With what…

A: Given : Horizontal speed (vox) = 12 m/s Initial position of stone (yo) = 10 m Final position (y) = 0…

Q: A ball is projected vertically upward with a velocity of 40m/sec. Three seconds later a second ball…

Q: In a downhill ski race, your final velocity is not affected very much by getting a running start,…

A: The given quantities are

Q: The elevations of the ski jumping hill shown below are as follows: hA = 46 m hB = 2.4 m hC = 6.8 m…

Q: if the ball is thrown an angle of 25° relative to the ground and is

Q: A roadrunner is cruising at 14 m/s without knowing the road under its feet is about to run out, at…

A: The roadrunner is moving with a constant initial velocity of 14 m/s. It then comes at the end of a…

Q: (a) A spaceship is projected vertically upward from the Earth's surface with an initial speed of…

Q: a projectile was fired at an angle of 45 degrees to the horizontal plane at a speed of 300m/s. how…

A: At the highest point of projectile motion, vertical component is zero and horizontal component…

Q: A very bored 318 kg bear decides to jump across a stream. The stream is 6 m wide and the east bank…

A: First, we need to identify the variables from the problem. The bear's initial velocity vi is given…

Q: The known elevations of the ski jumping hill shown below are as follows: hB = 1.5 m hC = 7.5 m If…

Q: The known elevations of the ski jumping hill shown below are as follows: hB = 2.0 m hC = 7.0 m If…

A: Energy Conservation- The total energy of the system remains constant throughout the motion, it can…

Q: An object moving horizontally approaches an edge of a cliff with the unknown speed v. What is the…

Q: An object is thrown horizontally from a height of 3 m with a speed of 18 m/s. If air resistance is…

A: Initial height (h) = 3 m Initial horizontal velocity (u) = 18 ms

Q: Helen, who is bored at home, amuses herself by throwing paper balls into the trash can. She makes…

A: Given, velocity of paper ball v = 5.8 m/s angle at which it throw above the horizontal θ = 33°…

Q: On a dare from a friend, you decide to try to jump a canyon using your bicycle as shown in the…

Q: A cannon boys shot out of a cannon 400 m above ground at a speed of 50 m/s 80 launch angle 40° .what…

A: Given data The height above the ground from which the cannon is shot is H = 400 m. The speed of the…

Q: A small ball rolls horizontally off the edge of a tabletop that is 1.20 m high. It strikes the floor…

A: Given: height of the table, h = 1.20 m horizontal distance of the striking point from the…

Q: What initial velocity v0 is required for a bullet, fired vertically from ground level, to reach a…

A: Initial velocity v0 (to be evaluated)The final velocity vf=0m/s (At the maximum height it will come…

Q: A ball is thrown 6ft above the ground at 40mph with a 45 degree angle. The ball is caught 9 feet…

A: Given Initial speed of ball, u = 40 mph = 17.88 m/s Ball thrown from a height, h = 6ft = 1.828…

Q: A roadrunner is cruising at 6 m/s without knowing the road under its feet is about to run out, at…

Q: A projectile is launched at a height of 20 m at an angle of 40 degrees, with what speed must it…

Q: A ball was thrown horizontally from a height of 32m.What initial speed is needed for the ball to…

Q: A roller coaster cart is initially moving at a speed of 1.80 m/s when it is at height h. When it…

Concept explainers

Projectile Motion

Topic Video

Question

**Projectile Motion Problem**

**Problem Statement:**

A ball is thrown at an angle of 30° from the top of a building 0.10 km high. The ball strikes the ground at a point 125 m horizontally away from and below the point of release.

**Questions:**

(a) What is the initial speed of the ball?

(b) What is the speed of the ball just before it strikes the ground?

**Instructions for Solving:**

1. **Understand the given information:**
- Angle of projection, \( \theta = 30^{\circ} \)
- Height of the building, \( h = 0.10 \, \text{km} = 100 \, \text{m} \)
- Horizontal distance from the point of release to the point where the ball hits the ground, \( R = 125 \, \text{m} \)

2. **Break down the components of the projectile motion:**
- Decompose the initial velocity \( v_0 \) into horizontal (\( v_{0x} \)) and vertical (\( v_{0y} \)) components:
- \( v_{0x} = v_0 \cos 30^{\circ} \)
- \( v_{0y} = v_0 \sin 30^{\circ} \)

3. **Use the kinematic equations to solve for the initial speed \( v_0 \):**
- Horizontal motion:
\[ R = v_{0x} t \]
\[ 125 = v_0 \cos 30^{\circ} \times t \]
- Vertical motion:
- Use the equation for displacement:
\[ y = v_{0y} t - \frac{1}{2} g t^2 \]
\[ -100 = (v_0 \sin 30^{\circ})t - \frac{1}{2} g t^2 \]

4. **Solve the system of equations to find \( t \) (time of flight) and \( v_0 \):**

5. **Calculate the final speed of the ball just before it strikes the ground:**
- Use the equations for horizontal and vertical components of velocity just before impact:
- \( v_{x} = v_{0x} \)
- \( v_{y} = v

Expert Solution

This question has been solved!

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

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step 7

Step by step

Solved in 7 steps with 7 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

The egg is launched at a speed of 49 m/s at an angle of 63 degrees above the horitzonal. At what height should a portal be placed in order to intercept the egg at its highest point above the ground?
A ball is thrown horizontally from a height of 20 m and hits the ground with a speed that is three times its initial speed. What is its initial speed?
A projectile is thrown from the top of a building with an initial velocity of 300m/s in the horizontal direction. If the top of the building is 30m above the ground, how fast will the projectile be moving just before it strikes the ground?
A projectile is thrown from the top of a cliff with an initial speed of 25 m/s at an angle of 600 up from the horizontal. If the projectile lands 100 m from the base of the cliff how tall is the cliff?
An extreme sports enthusiast runs at 4 m/s horizontally as she leaps off of the 830 meter tall Burj Khalifa. When she is 200 m from the ground, she opens her parachute. How far away is she from the building when her parachute opens? Please round to the nearest meter
Before jumping from the bridge, Martin throws his water bottle to a friend standing on the bank of the lake. The bridge is 7.0 m high. The friend is standing on the bank 15.0 m from the base of the bridge with their hand 1.0m above the ground. What speed must Martin throw the bottle horizontally for it to reach his friend's hand?
A daredevil is attempting to jump his motorcycle over a line of buses parked end to end by driving up a ramp of 61.8 degrees at a speed of 49 m/s. What would be the largest number of buses he can clear if the top of the takeoff ramp is at the same height as the bus tops and the buses are 10.0 m long? Use g = 9.8 m/s?. Your answer should be in the form of an integer number (e.g., 3 buses, not 3.4 buses).
A particle starts from the origin at t = 0 with a velocity of (16 - 12) m/s and moves in the xy plane with a constant acceleration of = (3.0 - 6.0) m/s2. What is the speed of the particle at t = 2s?
A daredevil is attempting to jump his motorcycle over a line of buses parked end to end by driving up a ramp of 27.7 degrees at a speed of 42.3 m/s. What would be the largest number of buses he can clear if the top of the takeoff ramp is at the same height as the bus tops and the buses are 10.0 m long? Use g = 9.8 m/s?. Your answer should be in the form of an integer number (e.g., 3 buses, not 3.4 buses).
A ball is thrown horizontally from the top of a building 74 m high. The ball strikes the ground at a point 90 m horizontally away from and below the point of release. What is the speed of the ball just before it strikes the ground? (note: speed is magnitude of velocity at that point).
A medieval city has the shape of a square and is protected by walls with length 500 m and height 15 m. You are the commander of an attacking army and the closest you can get to the wall is 100 m. Your plan is to set fire to the city by catapulting heated rocks over the wall (with an initial speed of 80 m/s ). At what range of angles should you tell your men to set the catapult? (Assume the path of the rocks is perpendicular to the wall.)
A police officer is chasing a burglar across a rooftop. Both are running at a speed of 5 m/s. Before the burglar approaches the edge of the roof, the burglar needs to make a decision about whether to jump the gap to the next building, which is 6.5 m away but 6.0 m lower. Will the burglar be able to land on the next building on his or her feet (assuming that the burglar’s initial velocity is 5 m/s horizontally when the jump begins)?