Atoy rocket is launched at an initial velocity of 50 ft/s at an angle of 75° with the horizontal. how long will it take for the rocket to travel 20 feet horizontally?

t = 1.55 sec

Step-by-step explanation:

Because we are asked to find the time it will take for the rocket to travel horizontally, we are only concerned with the x-dimension here.  

We are told that the initial velocity is 50 ft/s and the angle is 75 degrees.  

The equation we are going to need to solve this involves the displacement, the initial velocity, the acceleration, and the time...all in the x dimension:

Δx = V₀t + 1/2at²

We have the displacement, we can solve for the initial velocity, we know acceleration, and time is what we are solving for.

Let's work to fill in these values:

Δx = 20 feet

V₀x = V₀ cos Ф (that's the closest thing I could find to theta)

a = 0 (acceleration is always 0 in the horizontal dimension)

t = ?

From the information we can determine the initial velocity in the x dimension using the formula

Solving for the initial velocity in the x-dimension:

, which gives us from our calculators that initial velocity in the x-dimension is 12.941 (I am not paying attention to significant digits here since 50 has only 1).

Now we can fill in our equation with the info:

Because a = 0, the whole portion of the equation after the plus sign equals 0, so we can disregard and simply solve:

20 = 12.941t so

t = 1.55 seconds

the ratios are reciprocals im positive

step-by-step explanation:

they are all positive numbers so it wouldn't be the other ones