Question

A person stands on the ground with a slingshot and tries to hit a high limb on a nearby tree. The limb is 23.8 feet above the ground. What is the minimum initial velocity in meters/second of a rock leaving the slingshot at 6 feet above the ground that would be able to reach the limb? Note: Convert units as necessary.

Answer 1

The minimum initial velocity is 10.31 m/s.

Step-by-step explanation:

Given that,

Length = 23.8 feet

We need to calculate the height of the limb from the sling

`h=23.8-6=17.8\ feet`

Using conservation of energy theorem

`M.E_(i)=M.E_(f)`

`P.E_(i)+K.E_(i)=P.E_(f)+K.E_(f)`

`0+(1)/(2)m(v_(f)^2-v_(i)^2)=mgh+0`

`(1)/(2)m(v_(f)^2-v_(i)^2)=mgh`

At position of limb, final velocity is zero.

`v_(f)=0`

Put the value into the formula

`(1)/(2)v_(i)^2=gh`

`v_(i)=√(2gh)`

Put the value into the formula

`v_(i)=√(2*9.8*5.42544)`

`v_(i)=10.31\ m/s`

Hence, The minimum initial velocity is 10.31 m/s.