Trinity is throwing a tennis ball up in the air from the ground. Trinity is 5 feet tall, and is throwing the ball straight up with an initial speed of 64 feet per second. The function: f(t) = −16t 2 + 64t + 5, where t represents time in seconds, models this situation.

1. Trinity’s friend Max is in an apartment building that is next to where Trinity is throwing the ball. He is taking action pictures of the ball from his window. Max is able to take pictures when the height of the ball is more than 50 feet above Trinity.

A. Use the information here and the given function above to write an inequality to represent this problem situation. (Hint: If Trinity is 5 feet tall, what would 50 feet above her be measured from the ground?)

B. Determine the time period (t) range when Max will be able to take pictures of the ball. (Use desmos to graph your inequality as two different equations, find their intersection and sketch your graph here:)

Sketch:

Time Period :

2.Max wants to take a picture when the ball reaches its maximum height.

A. What is the Maximum height of the ball?

B. At What time (t) should Max take a picture of the ball? (HInt: What is the t value at your maximum height)

C. Consider that the window in the building is 55 feet above the ground. What is the vertical distance between the Max in the window and the maximum height of the ball?