GOZUNTA
Try it now
All courses Algebra I · F-LE.6 73 of 76
Apply quadratic functions to physical situations such as projectile motion under gravity.

Identify the initial height from a projectile function

Problem
Identify the initial height in projectile function \(h(t)=-16t^2+48t+5\).
Your answer
Show answer choicesHide answer choices Work through the mathematics first, then compare your reasoning.Select the answer that matches your work.
With a free account

Try the session again.

Return to a past session and redo it when you want another look at the same skills.

Create a free account
With paid access

Open the complete course.

A subscription unlocks every problem type and variant in your selected course, not only the starter set.

Compare plans

Hint

Set \(t=0\) to find the starting height of the projectile.

In a projectile model, the initial height is \(h(0)\), which is the constant term when the function is expanded.

Solution walkthrough

01

Interpret initial height

\[\text{initial}~\text{time}~t=0\]

The initial height is the projectile's vertical position at the launch instant, so evaluate h at zero seconds.

02

Substitute the launch time

\[h(0)=-16(0)^2+48(0)+5\]

Every value comes from the supplied model, with 0 seconds substituted for t.

03

Simplify

\[h(0)=0+0+5=5\]

Both time-dependent terms vanish at launch, leaving the constant term.

04

State the result with units

\[\text{initial}~\text{height}=5~\text{feet}\]

The output h measures height, and the projectile coefficients use feet and seconds, so the linear unit is feet.

+

Another way

  1. In h(t)=at²+bt+c, the vertical intercept and initial height are c.

!

Common mistake

Do not report 48 as the initial height. That coefficient represents initial velocity; the height at t=0 is the constant 5.

Solution walkthrough video