Question

Orlando built a water rocket for a science experiment. He will launch it off the ground of the football field with an initial velocity of 88 feet per second. He wants to know when the water rocket will be the same height as the top of the football goal post, which is 30 feet tall. Which of the following statements are true? Select all that apply.

A) The rocket is the same height as the goal post at 0.365 seconds.

B) The rocket is the same height as the goal post at 5.822 seconds.

C) The equation -16t^2 + 88t + 30 = 0 could be used to solve the situation.

D) The rocket is the same height as the goal post at 5.135 seconds.

E) The step t = -88 - 77/44 - 1920 - 32 could be used to solve this situation

Answer 1

Orlando's water rocket's height matches that of the football goal posts when solving the quadratic equation -16t^2 + 88t - 30 = 0, which takes into account the initial velocity, gravitational acceleration, and height of the goal posts. Once the correct times are calculated, they indicate the moments when the rocket is at the desired height.

Step-by-step explanation:

Orlando built a water rocket and wants to know when it will be the same height as the top of the football goal post, which is 30 feet tall. To find out when the water rocket will be 30 feet high, we can use the motion equation for a projectile.

The equation for the vertical motion of the rocket is given by -16t^2 + 88t + 0 = 0, where -16 is half the gravitational acceleration in feet per second squared (32 ft/s2), 88 is the initial velocity in feet per second, and 't' represents time in seconds. To find when the rocket will reach the height of the goal posts, we will adjust the equation to -16t^2 + 88t - 30 = 0, where the -30 represents the height of the goal posts.

Using the quadratic formula to solve for 't' will give two possible times at which the rocket is 30 feet above the ground: once while going up and once while coming down. We discard any negative time solutions since they are not physically meaningful.