Question

a rocket is launched from the top of an 8-foot ladder. It’s initial velocity is 128 feet per second, and it is launched at an angle of 60* with respect to the ground, write parametric equations that describe the motion of the rocket as a function of timeX=(v cos ?)ty= (v sin ?)t+k -16^2?= beta sign

Answer 1

We know that:

- a rocket is launched from the top of an 8-foot ladder.

- It’s initial velocity is 128 feet per second, and it is launched at an angle of 60* with respect to the ground

And we must write parametric equations that describe the motion of the rocket as a function of time

To write the parametric equations we need to know that the parametric general equations for a Projectile Motion are:

`\begin{gathered} x=\left(v_0cos\theta\right)t \\ y=h+\left(v_0sin\theta\right)t-16t^2 \end{gathered}`

Where,

v0 represents the initial velocity

h represents the initial height

θ represents the angle respect to the ground

In our case,

`\begin{gathered} v_0=128(feet)/(sec) \\ h=8feet \end{gathered}`

Finally, replacing in the parametric equations:

`\begin{gathered} x=\left(128cos60\degree\right)t \\ y=8+\left(128sin60\degree\right)t-16t^2 \end{gathered}`

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