# 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 BYJU'S Exam Prep

Updated on: September 25th, 2023

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

### Derivation of Equation of Motion

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

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

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

Summary:

## 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.

A ball is hurled 49 meters per second vertically up in the air. It takes 5s to reach the earth’s surface in its entirety. The equation of motion formula can be derived using the calculus method, graphical method, and simple algebraic method.

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