Question

A hammer is dropped and it falls for 9 seconds 9 seconds before hitting the ground. Determine how far it falls, assuming an acceleration due to gravity of − 9.8 m/s 2 −9.8 m/s2 and no wind resistance.

Answer 1

The hammer falls a distance of 44.1 meters.

Step-by-step explanation:

Acceleration due to gravity is a constant value of -9.8 m/s2. When an object falls freely, it experiences uniform acceleration. In this case, the hammer falls for 9 seconds.

Step 1: Identify known values

• Acceleration due to gravity (a) = -9.8 m/s2
• Time (t) = 9 seconds
• Initial velocity (vi) = 0 m/s (hammer is dropped)

Step 2: Use the formula

The formula to calculate the distance fallen is: d = vit + 0.5at2

Step 3: Plug in the values and solve

d = (0 m/s)(9 s) + 0.5(-9.8 m/s2)(9 s)2

d = -44.1 m

Step 4: Final answer

The hammer falls a distance of 44.1 meters.

Answer 2

396.9 meter

Step-by-step explanation:

If a represents the acceleration,

Then according to the question,

a = -9.8 m/s²,

`(dv)/(dt)=-9.8` ( acceleration = change in velocity with respect to time ),

`dv = -9.8dt`

Integrating both sides,

`v=-9.8t + C`

When t = 0 seconds, v = 0 m/s,

`0 = -9.8(0) + C`

`\implies C = 0`

`\implies v=-9.8t`

`(dx)/(dt)=-9.8t` ( velocity = change in position with respect to time ),

`dx = -9.8tdt`

Integrating again,

`x=-4.9t^2 + C'`

When t = 0 , x = 0 meters,

`0=-4.9(0) + C'\implies C'=0`

Hence, the final equation that shows the position of the hammer after t seconds,

`x=-4.9t^2`

If t = 9 seconds,

`x = -4.9(9)^2 = -4.9(81) = -396.9` ( negative sign shows the fall ),

Therefore, it will fall 396.9 meter in 9 seconds