An object is allowed to free fall from rest from a height of 9 m. What will be its velocity on striking the ground?

An object is allowed to free fall from rest from a height of 9 m. What will be its velocity on striking the ground?

• A. 14.07 m/s
• B. 14.00 m/s
• C. 13.53 m/s
• D. 13.29 m/s

Answer: (D)

To determine the velocity of an object in free fall just before it strikes the ground, we can use the kinematic equation that relates initial velocity, acceleration due to gravity, distance fallen, and final velocity. The relevant equation is: \[ v^2 = u^2 + 2as \] where: - \( v \) is the final velocity, - \( u \) is the initial velocity (which is 0 m/s for an object starting from rest), - \( a \) is the acceleration due to gravity (approximately \( 9.81 \, m/s^2 \)), - \( s \) is the distance fallen (which is 9 m in this case). Substituting the known values into the equation, we have: \[ v^2 = 0^2 + 2 \cdot 9.81 \cdot 9 \] Calculating the right side: \[ v^2 = 2 \cdot 9.81 \cdot 9 \] \[ v^2 = 176.58 \] Taking the square root to find \( v \): \[ v = \sqrt{176.58} \approx 13

To determine the velocity of an object in free fall just before it strikes the ground, we can use the kinematic equation that relates initial velocity, acceleration due to gravity, distance fallen, and final velocity. The relevant equation is:

[

v^2 = u^2 + 2as

]

where:

• ( v ) is the final velocity,

• ( u ) is the initial velocity (which is 0 m/s for an object starting from rest),

• ( a ) is the acceleration due to gravity (approximately ( 9.81 , m/s^2 )),

• ( s ) is the distance fallen (which is 9 m in this case).

Substituting the known values into the equation, we have:

[

v^2 = 0^2 + 2 \cdot 9.81 \cdot 9

]

Calculating the right side:

[

v^2 = 2 \cdot 9.81 \cdot 9

]

[

v^2 = 176.58

]

Taking the square root to find ( v ):

[

v = \sqrt{176.58} \approx 13