A ball is thrown vertically upwards with a velocity of 49 m/s. Calculate the total time it takes to return to the surface of the earth.

By Ritesh|Updated : November 7th, 2022

A ball is thrown upwards vertically with 49 m/s velocities. The total time to return to the earth’s surface is 5s. Steps to Calculate the total time it takes to return to the surface of the earth.

Step 1: Given Data:

The final velocity of the ball v = 0

Let the time taken go up by t.

The initial velocity of the ball u = 49 m/s

Let the acceleration due to gravity be g = 9.8 m/s2

Step 2: Calculate the Height:

Newton's first equation of motion states that:

v = u - gt

Since the ball is moving uphill against the force of gravity, acceleration is indicated as negative.

0 = 49 - 9.8 x t

49 = 9.8t

t = 49/9.8

t = 5s

As a result, the total amount of time needed to return to the earth's surface = 2t = 2 x 5 = 10s

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Derivation of Equation of Motion

The following techniques can be used to obtain the equations of motion:

Equations of motion are derived using the simple algebraic method.
Motion equations are derived using a graphical method
Motion equations derived using the calculus method

As a result, it takes the ball 5 seconds to return to the earth's surface.

Summary: