When a ball is thrown up into the air, it makes the shape of a parabola. The equation S= -5t^2 + v*t + k gives the height of the ball at any time, t in seconds, where “v” is the initial velocity (speed) in meters/sec and “k” is the initial height in meters (as if you were on top of a tower or building).
Make up a scenario where a ball is thrown, shot, etc. into the air. You can choose any initial velocity (in meters/sec) and any initial height (in meters) of the ball, but include them in your written scenario. The ball can leave your hand, the top of a building, etc. so you can use many different values for the initial height.
S=-16t^2+v*t+k
Scenario: A Ball Thrown from a Rooftop
Let's consider a scenario where a ball is thrown from the rooftop of a building. The ball is initially held by a person standing on the roof of a 20-meter tall building.
Given information:
Initial velocity, v = 15 meters/sec
Initial height, k = 20 meters
Situation:
The person standing on the rooftop decides to throw the ball upwards with an initial velocity of 15 meters/sec. They release the ball from the edge of the rooftop and observe its motion.
To analyze the motion of the ball, we can use the equation S = -5t^2 + vt + k, where S represents the height of the ball at any given time t in seconds.
Using the given values, the equation becomes:
S = -5t^2 + 15t + 20
This equation allows us to calculate the height of the ball at any given time during its motion.
For example, let's find the height of the ball 2 seconds after it was thrown.
To find the height at t = 2 seconds:
S = -5(2)^2 + 15(2) + 20
S = -5(4) + 30 + 20
S = -20 + 30 + 20
S = 30 meters
Therefore, 2 seconds after being thrown, the ball reaches a height of 30 meters above the initial position on the rooftop.
By plugging in different values of time, we can track the height of the ball throughout its trajectory, forming the shape of a parabola. This equation helps us understand the ball's motion in terms of time, velocity, and initial height.