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The problem provides a formula for the height \( h(t) \) of a projectile, given by:

\[
h(t) = -4.9t^2 + v_0 t + h_0
\]

where:
- \( t \) is the time in seconds,
- \( v_0 \) is the initial velocity (in meters per second),
- \( h_0 \) is the initial height (in meters).

The task is to complete the equation for the height of an object after 4 seconds, given:
- \( h_0 = 11 \) meters,
- \( v_0 = 88 \) m/s.

### Step-by-Step Solution

1. Substitute \( t = 4 \), \( v_0 = 88 \), and \( h_0 = 11 \) into the formula:

   \[
   h(4) = -4.9 \cdot (4)^2 + 88 \cdot 4 + 11
   \]

2. Calculate each term:
   - \( -4.9 \cdot (4)^2 = -4.9 \cdot 16 = -78.4 \)
   - \( 88 \cdot 4 = 352 \)
   - The initial height \( h_0 = 11 \)

3. Combine these values:

   \[
   h(4) = -78.4 + 352 + 11
   \]

4. Perform the addition:

   \[
   h(4) = 284.6
   \]

### Answer
The completed equation with the values filled in is:

\[
h(4) = -4.9 \cdot (4)^2 + 88 \cdot 4 + 11
\]

And the calculated height at \( t = 4 \) seconds is \( 284.6 \) meters.

Do you want further details on any step or have any questions?

### Related Questions to Explore
1. How would the height equation change if the initial velocity was negative?
2. What would happen to the height if the initial height \( h_0 \) were zero?
3. How does gravity (the -4.9 factor) affect the height over time?
4. What would the equation look like if we wanted the maximum height?
5. How can we find the time at which the projectile hits the ground?

### Tip
For projectile motion, always separate the effects of initial velocity, gravity, and initial height to understand their individual contributions to height over time.

Complete the equation to show the height of an object after 4 seconds, thrown from an initial height of 11 meters with a velocity of 88 m/s, using the formula h(t) = -4.9t^2 + v0t + h0.

Learn to calculate the height of an object after 4 seconds when thrown with an initial velocity of 88 m/s from a height of 11 meters using the projectile motion formula h(t) = -4.9t^2 + v0t + h0. A step-by-step substitution approach makes it suitable for high school students.

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