Question

Question #af942

Answer 1

`t=3.6s`, rounded to one decimal place.

Explanation:

Using FPS system of units.

The kinematic expression is
`h(t)=h_0+ut+1/2g t^2`
Inserting given values and noting that acceleration due to gravity`32ft cdot s^-2` is acting against the direction of motion we get

`h(t)=7+54t+1/2(-32) t^2`
`h(t)=7+54t-16 t^2`
Which is the given equation.
-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.
We can start solution from here.

When the ball reaches ground `h=-7ft`
Inserting in the given height equation we get
`-7=7+54t-16 t^2`
`=>16 t^2-54t-14=0`
`=>8 t^2-27t-7=0`

Solving the quadratic with the inbuilt graphic tool we get two roots as below. Ignoring the `-ve` root as time can not be negative we get

`t=3.6s`, rounded to one decimal place.