A ball thrown vertically up form the top of a tower, with a...

A ball thrown vertically up form the top of a tower, with a velocity of $30 \mathrm{~m} \mathrm{~s}^{-1}$ reaches ground in $8 \mathrm{~s}$. Then (a) maximum height reached from ground is $45 \mathrm{~m}$. (b) velocity of the ball when it reaches ground is $50 \mathrm{~m} \mathrm{~s}^{-1}$. (c) height of the tower is $80 \mathrm{~m}$. (d) height of the tower is $90 \mathrm{~m}$.

A ball thrown vertically up form the top of a tower, with a velocity of $30 \mathrm{~m} \mathrm{~s}^{-1}$ reaches ground in $8 \mathrm{~s}$. Then
(a) maximum height reached from ground is $45 \mathrm{~m}$.
(b) velocity of the ball when it reaches ground is $50 \mathrm{~m} \mathrm{~s}^{-1}$.
(c) height of the tower is $80 \mathrm{~m}$.
(d) height of the tower is $90 \mathrm{~m}$.

Key Concepts

Maximum Height Determination

This concept involves finding the peak of a projectile's path, where its vertical velocity becomes zero before it begins descending. It is typically calculated using kinematic formulas that incorporate the initial velocity and the constant acceleration due to gravity.

Time of Flight Analysis

Time of flight analysis involves determining the total duration an object is in motion before it reaches a certain point. In problems involving vertical projectile motion with an initial height, the total time includes the time taken to rise to the maximum height and the time taken to fall to the ground.

Impact Velocity Calculation

Impact velocity calculation is used to compute the speed of a projectile as it reaches a particular point, such as the ground. This involves applying kinematic equations that take into account the total displacement over the time of flight with the acceleration due to gravity.

Kinematic Equations

These are a set of equations used to relate displacement, initial velocity, final velocity, acceleration, and time in the study of motion. They are fundamental tools in analyzing the motion of projectiles under constant acceleration.

Uniform Acceleration

This concept refers to motion in which the acceleration remains constant throughout the time interval considered. In the context of projectile motion under gravity, it means that the only acceleration acting on the object is the constant acceleration due to gravity.

Projectile Motion

Projectile motion involves the movement of an object thrown into space, where it is subject only to gravitational acceleration (neglecting air resistance). It requires analyzing both the upward (ascend) and downward (descend) portions of the trajectory.

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