Questions: If an object is projected upward with an initial velocity of 123 ft per sec, its height h after t seconds is h=-16t^2+123t. Find the height of the object after 4 seconds. The height of the object after 4 seconds is ft.

If an object is projected upward with an initial velocity of 123 ft per sec, its height h after t seconds is h=-16t^2+123t. Find the height of the object after 4 seconds.

The height of the object after 4 seconds is ft.

Transcript text: If an object is projected upward with an initial velocity of 123 ft per sec , its height $h$ after $t$ seconds is $h=-16 \mathrm{t}^{2}+123 \mathrm{t}$. Find the height of the object after 4 seconds. The height of the object after 4 seconds is $\square$ ft.

Solution

Solution Steps

Step 1: Understand the Problem

We are given the height function of an object projected upward: \[ h(t) = -16t^2 + 123t \] We need to find the height of the object after 4 seconds.

Step 2: Substitute the Time into the Height Function

Substitute \( t = 4 \) into the height function: \[ h(4) = -16(4)^2 + 123(4) \]

Step 3: Calculate the Height

First, calculate \( 4^2 \): \[ 4^2 = 16 \]

Now substitute back into the equation: \[ h(4) = -16(16) + 123(4) \]

Calculate each term: \[ -16 \times 16 = -256 \] \[ 123 \times 4 = 492 \]

Add the results: \[ h(4) = -256 + 492 = 236 \]

Final Answer

The height of the object after 4 seconds is \(\boxed{236}\) ft.

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >

Thank you for your feedback.

Copied!