Question

You throw a ball to your friend. The ball leaves your hand 5 feet above the ground and has an initial velocity of 50 feet per second. Your friend catches the ball when it falls to a height of 3 feet. Write a vertical motion model that represents this situation. How long is the ball in the air?

Answer 1

To represent the vertical motion of the ball, use the equation h = -16t^2 - 50t + 5. To find how long the ball is in the air, set h equal to 3 and solve for t.

Step-by-step explanation:

To write a vertical motion model that represents this situation, we need to consider the ball's height above the ground and its initial velocity. Let's assume the positive direction is upward.

The equation for vertical motion can be written as:

h = -16t^2 + v0t + h0

Where:

• h is the height of the ball above the ground
• t is the time
• v0 is the initial vertical velocity (in this case, -50 ft/s since the ball is thrown upward)
• h0 is the initial height (in this case, 5 ft)

If we plug in the values, the equation becomes:

h = -16t^2 - 50t + 5

To find how long the ball is in the air, we need to find the time when the ball's height is 3 ft. We can set h equal to 3 and solve for t:

-16t^2 - 50t + 5 = 3

-16t^2 - 50t + 2 = 0

We can solve this quadratic equation using the quadratic formula or factoring method. Once we find the values of t, we can determine how long the ball is in the air.