Question

If a projectile is shot at an angle of `pi/3` and at a velocity of `26 m/s`, when will it reach its maximum height??

Answer 1

`t=2.3` seconds rounded to 1 decimal place

Explanation:

The maximum height is when the vertical velocity component of the projectile is equal to the vertically downward velocity due to gravity.

Thus we have the model:

`=> Rsin(theta)="g"t`

Where
`R= 26m/s`
`theta=pi/3`
`g~~9.81 m/s^2 larr" known"`

`t` is time in seconds

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

This becomes:

`=>26color(red)(m/s)sin(pi/3)=9.81color(red)(m/s^2)color(white)(.)t`

You manipulate the units in the same way you do the numbers

`=>t= 26/9.81 sin(pi/3)color(red)( xx(cancel(m))/(cancel(s))xxs^(cancel(color(white)(.)2))/(cancel(m)) larr" dealing with the units")`

`t=2.29527...` seconds

`t=2.3` seconds rounded to 1 decimal place