Question

gary kicks a field goal with an inital veritcal velocity of 38m/s how long will it take the football to hit the ground

Answer 1

The ball reaches the ground after 7.76 s

Step-by-step explanation:

The motion of the ball along the vertical direction is a free fall motion, which is affected by the force of gravity only; therefore it is a uniformly accelerated motion (=constant acceleration), so we can use the following suvat equation:

$s=ut-\frac{1}{2}gt^2$

where

s is the displacement

u is the initial vertical velocity

$g=9.8 m/s^2$ is the acceleration due to gravity

t is the time

In this problem,

u = 38 m/s

Also, we want to find the time t at which the ball hits the ground again: so, when the displacement becomes zero again,

s = 0

Therefore the equation becomes:

$0=38t-\frac{1}{2}9.8t^2\\0=38t-4.9t^2$

And solving for t,

$t(38-4.9t)=0$

we have two solutions:

t = 0 (instant at which the ball is kicked)

$38-4.9t=0\\t=\frac{38}{4.9}=7.76 s$

which is the solution to the problem.

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