c) The rocket is launched a third time with the same initial velocity as before at an angle of 45 degrees. This time we want to launch the rocket so that it goes through a field goal post at a height of 7.9 meters in the air. Calculate the time the rocket will be in the air for. Calculate the horizontal distance in which the rocket must be placed from the field goal post.

Question

c) The rocket is launched a third time with the same initial velocity as before at an angle of 45 degrees. This time we want to launch the rocket so that it goes through a field goal post at a height of 7.9 meters in the air. Calculate the time the rocket will be in the air for. Calculate the horizontal distance in which the rocket must be placed from the field goal post.

(the initial velocity as before was 27.44.. when i multiply that by the sin and cos of 45 degrees i get 19.40301.. it's the same for each by the way.. so i use 19.40301 for the initial velocity for finding the time and horizontal distance.)

Answer 1

To calculate the time the rocket will be in the air, you can use the kinematic equation for vertical motion:

h = viy * t - (1/2) * g * t^2

Where:
- h is the height of the field goal post (7.9 m)
- viy is the vertical component of the initial velocity (which is equal to the initial velocity times sine of the launch angle)
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
- t is the time in seconds

Substituting the known values, we have:

7.9 = 19.40301 * t - (1/2) * 9.8 * t^2

Simplifying the equation, we get:

0 = 4.9 * t^2 - 19.40301 * t + 7.9

This is a quadratic equation in the form: at^2 + bt + c = 0

Now, we can solve this equation to find the time the rocket will be in the air. You can either use the quadratic formula or factorization method to solve for t. Once you find the two possible values for t, discard the negative solution as time cannot be negative.

To calculate the horizontal distance the rocket must be placed from the field goal post, you can use the kinematic equation for horizontal motion:

d = vix * t

Where:
- d is the horizontal distance
- vix is the horizontal component of the initial velocity (which is equal to the initial velocity times cosine of the launch angle)
- t is the time in seconds (which we calculated earlier)

Substituting the known values, we have:

d = 19.40301 * t

Now, you can substitute the value of t (from the previous step) into the equation to find the horizontal distance.