Question

50 POINTS...Which equation would best help solve the following problem? Tania releases a javelin 1.6 meters above the ground with an initial vertical velocity of 25 meters per second. How long will it take the javelin to hit the ground?

Answer 1

im doing the same quiz anyone know number 1 with the base of a traingle or something

Answer 2

Let
`x(t)` be the vertical position of the javelin at time
`t`. Once it's thrown in the air, the only force acting on it is gravity, so the javelin would be subjected to a constant downward acceleration of approx. 9.8 meters per second per second. So


`x''(t)=-9.8`

Integrating once with respect to
`t`, we get


`x'(t)=-9.8t+C_1`

where
`x'(t)` is the velocity of the javelin. We're told that
`x'(0)=25`, so


`25=-9.8\cdot0+C_1\implies C_1=25`

Integrating again with respect to
`x` to get


`x(t)=-4.9t^2+25t+C_2`

and we know the javelin was initially thrown 1.6 meters above the ground, or
`x(0)=1.6`, so we get


`1.6=-4.9\cdot0^2+25\cdot0+C_2\implies C_2=1.6`

So the javelin's position at any time
`t` is given by


`x(t)=-4.9t^2+25t+1.6`

It will hit ground when
`x(t)=0`. Solve this however you want; you'll find that this will happen at about
`t=5.165` seconds after the javelin has been thrown.