A ball is kicked off a pier and lands in the sea. The balls height T seconds after it was kicked is given by the equation h(T)=2/7x(T+3)(7-T) after how many seconds is the ball at the same height as the pier again

To find when the ball is at the same height as the pier again, we need to determine the time \( T \) when \( h(T) = 0 \). The height equation is given by:

\[ h(T) = \frac{2}{7} (T + 3) (7 - T) \]

We set \( h(T) = 0 \) and solve for \( T \):

\[ 0 = \frac{2}{7} (T + 3) (7 - T) \]

Since \(\frac{2}{7} \neq 0\), we can ignore the coefficient and focus on the product:

\[ (T + 3)(7 - T) = 0 \]

This product equals zero when either factor equals zero:

1. \( T + 3 = 0 \)
2. \( 7 - T = 0 \)

Solving these equations:

1. \( T + 3 = 0 \)
   \[ T = -3 \]

2. \( 7 - T = 0 \)
   \[ T = 7 \]

The ball cannot be at \( T = -3 \) because time cannot be negative. Therefore, the ball is at the same height as the pier again at \( T = 7 \) seconds.

Would you like more details on this solution or have any other questions?

Here are 5 more questions you might ask:

1. How do you find the maximum height the ball reaches?
2. What is the initial height of the ball when it was kicked?
3. Can you derive the time at which the ball reaches its maximum height?
4. What is the significance of the coefficients in the height equation?
5. How does the shape of the trajectory change with different coefficients?

**Tip:** When solving equations involving products, remember that any term multiplied by zero results in zero. Therefore, set each factor of the product to zero to find potential solutions.

Explore how to solve a quadratic equation representing the height of a ball kicked off a pier and landing in the sea. This problem involves quadratic equations and polynomials. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation