A particle is thrown vertically upwards. Its velocity at half of the height is 10m/s, then the maximum height attained by it will be: (g=10 m/s2)

By Ritesh|Updated : November 14th, 2022

(a) 10 m

(b) 20 m

(c) 15 m

(d) 25 m

A particle is thrown vertically upwards. Its velocity at half of the height is 10m/s, then the maximum height attained by it will be 10 m. Steps to find the maximum height attained by the particle is thrown vertically upwards:

Step 1: Given that

The acceleration due to gravity, g = 10 m/s2

Velocity at half of the height, v = 10 m/s

Step 2: calculating the equation of motion for a particle at half its height

Let h meters be the maximum height.

The equation of motion formulas allows us to determine:

v2 = u2 - 2gs

where s is the displacement, g is the acceleration caused by gravity, and v is the final velocity.

Substituting the values we get:

102 = u2 - 2g h/2

100 = u2 - gh …. (i)

Step 3: When the particle is at its highest point, find the equation of motion:

v = 0 when the height is greatest.

Substituting the value we get:

0 = u2 - 2gh

u2 = 2gh …. (ii)

Step 4: Using the equations I and (ii), get the maximum height:

The equation I results when the value of u2 is entered.

100 = 2gh - gh

100 = gh

h = 100/g

= 100/10

= 10 m

Summary:

A particle is thrown vertically upwards. Its velocity at half of the height is 10m/s, then the maximum height attained by it will be: (g=10 m/s2)

Vertically upwards, a particle is launched. If the object's speed at halfway up is 10 m/s, its highest point will be 10 m. The rate at which an object's position changes in relation to a frame of reference and time is what is meant by velocity.

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