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Questions and Answers
What is the height of the tower if a stone is dropped from the top and another stone is dropped from 20 m below it after 1 second, reaching the ground simultaneously? (Take g = 10 m/s²)
What is the ratio of average velocity to maximum velocity for a particle traveling first distance S with acceleration, then 2S with constant speed, and finally 3S with retardation?
If a body is thrown vertically upward and reaches the ground in t1 seconds, and downward with the same speed in t2 seconds, which of the following is correct?
What is the initial speed needed for a ball thrown from height H to hit the floor with a velocity of 10 m/s after 1.5 seconds?
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If a long horizontal belt moves at 2 m/s with two ink marks A and B 60 m apart, what is true regarding the time taken by an insect to travel from A to B compared to B to A?
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If the distance travelled by a particle in straight line motion is proportional to the square root of the time, the acceleration is proportional to which of the following?
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What is the distance traveled by a particle assuming constant acceleration, if it covers 10 m in the first 5 seconds and 10 m in the next 3 seconds?
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What will happen to a stone released from a balloon that rises with an acceleration of 1.25 m/s² after 8 seconds?
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What should be the throwing speed of balls so that more than two are in the air at any time if thrown vertically upwards every 2 seconds?
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What is the average speed of a man walking to a market 2.5 km away at 5 km/h, then back at 7.5 km/h, over 40 minutes?
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Study Notes
Question 4 - Freefall
- A stone is dropped from a tower of height h.
- After 1 second, another stone is dropped from a balcony 20 m below the top of the tower.
- Both stones reach the bottom simultaneously.
- The goal is to find the height of the tower h.
- Use the acceleration due to gravity g = 10 m/s².
Question 5 - Motion of a Particle
- A particle starts from rest and travels a distance S with uniform acceleration.
- It then travels a distance 2S with uniform speed.
- Finally, it travels a distance 3S with uniform retardation and comes to rest.
- The particle's motion is in a straight line.
- Determine the ratio of the average velocity to the maximum velocity.
Question 6 - Body Thrown Vertically
- A body is thrown vertically upwards from the top of a tower.
- It reaches the ground in t₁ seconds.
- The same body is thrown vertically downwards from the same point with the same speed.
- This time, it reaches the ground in t₂ seconds.
- Determine the time it takes for the body to reach the ground if it is simply dropped (with zero initial velocity) from the top of the tower.
Question 9 - Ball Thrown Vertically
- A ball is thrown from a height H.
- It hits the floor with a velocity of 10 m/s after 1.5 seconds.
- Find the initial speed of the ball.
- Utilize the information given, the acceleration due to gravity, and relevant kinematic equations to find the initial speed.
Question 10 - Projectile Motion
- In the scenario of the ball thrown from height H, calculate the angle of projection, represented by θ.
- Use the information from the previous question, including the initial speed and time of flight, to determine the angle.
- Utilize trigonometric functions and kinematic equations to calculate the angle.
Question 11 - Height of Projection
- Continuing the scenario of the ball thrown from height H, calculate the value of H.
- Utilize the information from the previous questions, including the initial speed, time of flight, and acceleration due to gravity.
- Apply relevant kinematic equations to solve for the initial height.
Question 12 - Insect on a Belt
- A long horizontal belt moves from left to right with a uniform speed of 2 m/s.
- Two ink marks, A and B, are on the belt, 60 m apart.
- An insect runs on the belt back and forth between the marks.
- The insect's speed relative to the belt is constant at 4 m/s.
Question 13 - Insect Motion on a Belt
- In the scenario of the insect on the belt, where mark A is to the left of mark B, analyze the time taken by the insect to travel from A to B and B to A.
- Consider the insect's relative speed to the belt and the belt's own motion.
- Determine if the time taken for each trip is equal, or if one takes longer than the other.
Question 14 - Time for Insect on Belt
- In the scenario of the insect on the belt, where A lies to the left of B, calculate the time taken by the insect to travel from B to A.
- Use the information about the insect's relative speed, the belt's speed, and the distance between the marks to find the time.
Question 15 - Acceleration in Straight Line Motion
- A particle travels in a straight line.
- The distance it travels is proportional to the square root of the time taken.
- Determine how the particle's acceleration is related to its velocity (denoted by v).
- Analyze proportionality relationships and kinematics to find the relationship between acceleration and velocity.
Question 16 - Distance Travelled
- A particle travels 10 m in the first 5 seconds and 10 m in the next 3 seconds.
- Assuming constant acceleration, calculate the distance covered in the next 2 seconds.
- Use kinematic equations and the information provided about distances and times to solve for the distance travelled in the next 2 seconds.
Question 17 - Balloon and Stone
- A balloon rises from the ground with an acceleration of 1.25 m/s².
- After 8 seconds, a stone is released from the balloon.
- Analyze the motion of the stone after its release, taking into account gravity and the initial upward velocity due to the balloon's motion.
- Determine the stone's displacement, distance covered in reaching the ground, time to reach the ground, and the moment it begins moving downwards.
Question 18 - Average Speed
- A man walks 2.5 km to the market at a speed of 5 km/h.
- He returns home with a speed of 7.5 km/h.
- Calculate the average speed of the man over the entire journey, taking into account the different speeds and distances traveled.
Question 19 - Balls Thrown Vertically
- A man throws balls vertically upwards with the same speed at intervals of 2 seconds.
- Determine the minimum required speed for the man to have more than two balls in the air at any given time.
- Consider the time it takes for a ball to ascend and descend, and the relationship between this time and the throwing interval.
- Use the acceleration due to gravity to analyze the motion of the balls.
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Description
This quiz covers key concepts in motion, including free fall, acceleration, and velocity. Solve problems involving a stone dropped from a height, a particle's motion under different conditions, and the effects of throwing a body upward and downward from a tower.
