Question

A lead pellet is propelled vertically upward by an air rifle with an initial speed of 16m/s. Find itsmaximum height.

Answer 1

13.06 m

Step-by-step explanation

The maximum height of an object that is thrown upward is reached when its velocity is zero. This is because the object stops for a moment before changing direction and start falling down.

First we have to find the time it takes for the pellet to reach the maximum height:

`v=u-gt`

u is the initial velocity 16m/s and g is the acceleration of gravity, which is negative because is opposite to the direction of motion. The final velocity v is zero, as stated before:

`0=u-gt`

Solving for t:

`\begin{gathered} u=gt \\ t=(u)/(g) \end{gathered}`

If we consider g = 9.8m/s²:

`t=(16m/s)/(9.8m/s^2)\approx1.63s`

Now we can find what is the height of the pellet at that time:

`y=ut-(1)/(2)gt^2`

Replacing with the information we have:

`y=16m/s\cdot1.63s-(1)/(2)\cdot9.8m/s^2\cdot1.63^2s^2=13.06m`

The pellet's maximum height is 13.06 m