1. A body is projected with a velocity, u = (3i + 4j) m/s. The maximum height attained by the body is (g = 10 m/s²)? 2. An aeroplane moving horizontally with a speed of 180 km/h dr... 1. A body is projected with a velocity, u = (3i + 4j) m/s. The maximum height attained by the body is (g = 10 m/s²)? 2. An aeroplane moving horizontally with a speed of 180 km/h drops a food packet while flying at a height of 490 m. The horizontal range is? 3. A particle is fired horizontally with a velocity of 100 m/s from the top of a hill 500 m high. What is the horizontal range of the projectile? 4. From the top of a tower 20 m high, a ball is thrown horizontally. If line joining the point of projection to the horizontal meets the ground makes an angle 45° with the horizontal, then the initial velocity of the ball is? 5. At the height of 800 m, an aeroplane is moving with 150 m/s. A bomb is dropped from it so as to hit its target. At what distance from the target should the bomb be dropped? 6. Three particles A, B and C are thrown from the top of a tower 100 m in height with the same speed 10 m/s. A is thrown straight up, B is thrown straight down and C is thrown horizontally. They hit the ground with the speeds uA, uB, and uC respectively. 7. When a projectile is fired at an angle θ with the horizontal with velocity u, then the horizontal component velocity of the projectile, ignoring air resistance? 8. In case of an angular projectile motion, what is the angle between the velocity and acceleration at the highest point? 9. A cricketer can throw a ball to a maximum horizontal distance of 100 m. How much high above the ground can the cricketer throw the same ball? 10. A missile is fired from maximum range with an initial velocity of 20 m/s. If g = 10 m/s², the range of the missile is? 11. During a projectile motion, if the maximum height equals to the horizontal range, then the angle of projection with the horizontal is? 12. A body is projected with velocity u so that its horizontal range is twice the greatest height attained. The value of range is? 13. Two projectiles are fired at different angles with the same magnitude of velocity, such that they have the same range. At what angles they might have been projected? 14. Range of a projectile is R, when the angle of projection is 30°. Then, the value of the other angle of projection for the same range is: 15. If the maximum range of a projectile during angular projection is R, then the greatest height attained by it is? 16. For the projectile, projected with velocity u making an angle θ with the horizontal, its range on a horizontal angle is (3/2)R when the maximum height attained is?
Understand the Problem
The question is related to projectile motion in a two-dimensional context, involving calculations of ranges, heights, and angles associated with the motion of projectiles. It seeks to understand various scenarios of motion given specific parameters.
Answer
The maximum height attained by the body is $0.8 \, \text{m}$.
Answer for screen readers
The maximum height attained by the body is $0.8 , \text{m}$.
Steps to Solve
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Understanding the problem We are focusing on the first question from the problem set regarding projectile motion. The equation of motion is given, and we need to find the maximum height attained by the body projected with a certain velocity.
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Identify the parameters The given velocity of the object is $$ \mathbf{u} = (3\hat{i} + 4\hat{j}) , \text{m/s} $$ which indicates the horizontal and vertical components of the velocity respectively.
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Calculate the vertical component of the velocity The vertical component of velocity ($u_y$) can be extracted from the initial velocity vector: $$ u_y = 4 , \text{m/s} $$
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Calculate the maximum height Using the kinematic equation for vertical motion under gravity: $$ H = \frac{u_y^2}{2g} $$ where $g = 10 , \text{m/s}^2$ is the acceleration due to gravity.
Substituting the vertical component: $$ H = \frac{(4)^2}{2 \cdot 10} = \frac{16}{20} = 0.8 , \text{m} $$
- Final calculation The calculation plainly reveals the maximum height attained by the body.
The maximum height attained by the body is $0.8 , \text{m}$.
More Information
The result indicates how high the projectile reaches vertically before it starts to descend due to gravity. This can be useful in various applications, such as determining safe distances for launching projectiles or designing sports equipment.
Tips
- Miscalculating the vertical component of the velocity by incorrectly reading the velocity vector.
- Forgetting to account for gravitational acceleration when using kinematic equations.
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