Question

A toy rocket is launched from the ground level with an initial vertical velocity of 96 ft/s. After how many

seconds will the rocket hit the ground

Answer 1

Answer:

  6 seconds

Step-by-step explanation:

You want to know how long it will take a rocket to hit the ground if it is launched from the ground level with an initial vertical velocity of 96 ft/s.

Ballistic motion

The equation usually used to describe the vertical component of ballistic motion is

  $h(t)=-\dfrac{1}{2}gt^2+v_0t+h_0$

where v₀ and h₀ are the object's initial vertical velocity and height, respectively. In customary units, the acceleration due to gravity (g) is approximated by 32 ft/s².

For an initial vertical velocity of 96 ft/s, the equation is ...

  h(t) = -16t² +96t = -16t(t -6)

Ground level

The value of h(t) is zero (ground level) when factors of the equation are zero: t = 0, and t = 6.

Since t=0 represents the launch time, the value t=6 represents the time the rocket returns to the ground.

The rocket will hit the ground after 6 seconds.