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Question

A ball thrown vertically upwards falls back on the ground after 6s, Assuming that the equation of motion is of the form s=ut4.9t2, where's' is in meter and 't' is in second, find the velocity at t=0


A

0m/s

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B

1m/s

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C

29.4m/s

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D

Noneofthese

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Solution

The correct option is C

29.4m/s


Step 1: Given data

At the highest point of a ball, the velocity of a ball will be equal to zero. Hence we have,

Initial velocity of a ball=u

Final velocity of a ball, v=0

Time taken by ball to return to the ground surface=6s

Hence, time taken to reach the highest position, t=3s

Given equation of motion is: s=ut-4.9t2

Displacement=s

Step 2: Calculating the velocity at t=0

We know that the velocity is equal to the rate of change of displacement. Hence,

v=dsdt=dut-4.9t2dtv=u-9.8t0=u-9.8tu=9.8t=9.8×3=29.4ms-1

Therefore initial velocity is equal to 29.4ms-1

Hence, option(C) is correct answer.


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