If Matt jumps from ground level with an initial velocity of 48 feet per second, how long does it take Matt to hit the ground?

Question

Vertical Motion Model:

 

Use the vertical motion model, which is s(t) = -16t² + vt + s, where v is your initial velocity, and s is your initial position. If Matt jumps from ground level with an initial velocity of 48 feet per second, how long does it take Matt to hit the ground?

Answer 1

Let's start by gathering the data we are given from the problem: initial velocity is 48 ft/sec and initial position is 0 ft.

Substituting these values into our equation, we now have:

s(t) = -16t²+48t+0.

Since we need to identify the time when Matt touches the ground, we must solve for t from the equation.

By using the quadratic formula, we can find that the solutions are: t=0 seconds and t= 3 seconds.

Based on logical reasoning, 0 seconds cannot be our solution as it's our starting point. Therefore, t=3 seconds is our answer: It took Matt 3 seconds to hit the ground given our conditions.

Answer 2

Matt hits the ground when

h(t) = 0 = -16t^2 +48t + s

if s=0 Matt hits the ground when

-16t^2 +48t = 0

-16t(t -3) = 0

t-3=0

t=3

in 3 seconds to hit the ground

or longer time, the larger s

-32t = 48

t =1.5 seconds to reach max height

max height = h(1.5) = -16(3/2)^2 +48(3/2)

= -36 +24(3)

= 72-36 = 36 feet = 3 yards

hopefully he lands on his feet and not his head

or medical bills could go far higher than he did,

through the roof

worse his basketball career may be over prematurely

or his Olympic gold in the long jump event

Answer 3