A ball thrown up vertically covers 25 m in its first one second of flight. Then (a) Initial vel

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A ball thrown up vertically covers 25 m in its first one...

A ball thrown up vertically covers $25 \mathrm{~m}$ in its first one second of flight. Then (a) Initial velocity $\mathrm{u}=30 \mathrm{~m} \mathrm{~s}^{-1}$ (b) Time of flight $=3 \mathrm{~s}$ (c) Maximum height $\mathrm{H}=45 \mathrm{~m}$ (d) Ratio of distance covered in the last second to the total distance of the flight is $\frac{5}{18}$

A ball thrown up vertically covers $25 \mathrm{~m}$ in its first one second of flight. Then
(a) Initial velocity $\mathrm{u}=30 \mathrm{~m} \mathrm{~s}^{-1}$
(b) Time of flight $=3 \mathrm{~s}$
(c) Maximum height $\mathrm{H}=45 \mathrm{~m}$
(d) Ratio of distance covered in the last second to the total distance of the flight is $\frac{5}{18}$

Key Concepts

Uniformly Accelerated Motion

This concept involves motion where the acceleration remains constant throughout the motion. In the context of projectile motion under gravity, the acceleration is due to gravity, and its constancy allows the use of standard kinematic equations to relate displacement, initial velocity, time, and acceleration. It is the fundamental basis for analyzing and predicting the behavior of objects under the influence of a uniform force such as gravity.

Kinematic Equations

These are mathematical formulas used to describe the relationships between displacement, initial velocity, time, and acceleration for objects moving with constant acceleration. Equations such as s = ut + 1/2at², v = u + at, and v² = u² + 2as are instrumental in solving problems related to projectile motion, including the determination of initial velocities, displacement over time intervals, and time of flight.

Vertical Projectile Motion

This subject covers the motion of objects that are thrown vertically upward under the influence of gravity. It includes determining parameters like maximum height, time of flight, and the variations in velocity and displacement over the course of the flight. Understanding vertical projectile motion hinges on applying the kinematic equations with gravitational acceleration taken as a constant value.

Time of Flight

In projectile motion, the total time an object stays in the air is referred to as the time of flight. It is determined by the initial velocity and the acceleration due to gravity. This concept is key to analyzing the entire duration of the motion from launch to when the object returns to its original position, and it helps in calculating other parameters such as maximum height and overall displacement.

Maximum Height

This is the peak point reached by an object thrown vertically upward, where its instantaneous velocity becomes zero. The maximum height can be calculated using the relationship between initial velocity and gravitational acceleration, typically by using the equation H = u²/(2g). It is a critical parameter in understanding the extent of the projectile's vertical motion.

Displacement Over Time Intervals

This concept involves computing the distance covered by an object during a specific time interval using the kinematic equations. It is particularly useful when analyzing segments of motion, such as determining how far an object travels in its first second or its last second. This allows for the comparison of partial displacements to the total displacement, providing deeper insights into the motion dynamics.

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