Answer:
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
[tex]V_{0x}=V_{0}cos(\theta)[/tex]
Solving for the initial velocity in the x-dimension:
[tex]V_{0x}=50cos(75)[/tex], 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:
[tex]20=12.941t+\frac{1}{2}(0)t^2[/tex]
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
