Question

5. A hammer is dropped from the top of atower that is 400 m high. If we neglect airresistance so that the only force on thehammer is gravity, with what velocity doesthe hammer strike the ground?

Answer 1

We wil have the following:

First, we will determine the travel time:

`400m=(0m)+(0m/s)t+(1)/(2)(9.8m/s^2)t^2\Rightarrow t^2=(2(400m))/((9.8m/s^2))`
`\Rightarrow t^2=(4000)/(49)s^2\Rightarrow t=\frac{20\sqrt[]{10}}{7}s`
`\Rightarrow t\approx9.0s`

Now, we find the velocity after that time:

`v=(0m/s)+(9.8m/s^2)(20\sqrt[]{10}/7s)\Rightarrow v=28\sqrt[]{10}m/s`
`\Rightarrow v\approx88.5m/s`

So, it will have approximately 88.5 m/s.