The only part of the height equation that we have not discussed is the constant. You have probably noticed that the constant is always equal to the initial height of the ball (80 m in our previous exercises). Now, let’s have you develop a height equation. A ball is thrown upward from the roof of a building 100 m tall with an initial velocity. When will the ball reach a height of 80 m
I will be happy to critique your thinking.
To develop a height equation for the given scenario, we need to understand the variables involved.
Let's denote:
- h as the height of the ball at any given time (in meters)
- h₀ as the initial height of the ball (100 m in this case)
- v₀ as the initial velocity of the ball (unknown)
- g as the acceleration due to gravity (approximately 9.8 m/s²)
The height equation for an object in free fall can be derived using the following formula:
h = h₀ + v₀t - (1/2)gt²
Since we want to find the time when the ball reaches a height of 80 m, we can substitute h = 80 into the equation:
80 = h₀ + v₀t - (1/2)gt²
However, we still have two unknowns, v₀ and t. To solve for both, we need more information.
Please provide the initial velocity of the ball, and I'll be happy to help you calculate the time it takes to reach a height of 80 m.