A ball is thrown vertically up with a velocity of 30 m / s at the edge of a 60-m cliff. Calculat

step 1 In this question we have speed v equals to 30 meter per second and initial height H0 equals to 6

A ball is thrown vertically up with a velocity of 30 m / s...

A ball is thrown vertically up with a velocity of $30 \mathrm{m} / \mathrm{s}$ at the edge of a $60-\mathrm{m}$ cliff. Calculate the height $h$ to which the ball rises and the total time $t$ after release for the ball to reach the bottom of the cliff. Neglect air resistance and take the downward acceleration to be $9.81 \mathrm{m} / \mathrm{s}^{2}$

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Key Concepts

Time of Flight Calculation

Determining the total time an object is in motion, especially when it reaches a particular height after being launched, often requires solving kinematic equations. In many cases, the equations reduce to a quadratic form, where the correct physical solution represents the time elapsed during the complete trajectory.

Maximum Height Determination

Calculating the maximum height reached by an object involves using kinematic equations and setting the velocity equal to zero at the peak of its trajectory. This method explains how the initial upward velocity is counteracted by gravitational pull until the object momentarily stops ascending.

Uniformly Accelerated Motion

This concept deals with the analysis of objects moving under a constant acceleration, typically expressed through kinematic equations that relate displacement, initial velocity, time, and acceleration. It is fundamental in describing the motion of a projectile under gravity.

Acceleration due to Gravity

Gravity provides a constant acceleration downward, which, when air resistance is neglected, is used to determine the change in velocity and displacement of objects in free fall or vertical motion. Its standard value is approximately 9.81 m/s² near the Earth’s surface.

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